The quasi-Newton method, like the Steepest Descent Methods, only requires the gradient of the objective function to be known at each iteration. By measuring the change in gradient, construct a model of the objective function that is sufficient to produce superlinear convergence. This class of methods outperforms the steepest descent method by a large margin, especially for hard problems. In addition, since the quasi-Newton method does not require second derivative information, it is sometimes more efficient than Newton's method. Today, optimization software includes a large number of quasi-Newton algorithms for solving unconstrained, constrained, and large-scale optimization problems. The quasi-Newton method is one of the most effective methods for solving nonlinear equations and optimization calculations. It is a kind of Newton-type iterative method that makes each iteration less computationally intensive while maintaining superlinear convergence [1].

Genetic Algorithm (GA) belongs to a branch of evolutionary computing, which was developed in the mid-1960s, it was proposed by John Holland of the University of Michigan in the United States and others, and flourished in the mid-1980s. The genetic algorithm is inspired by the biological evolution of nature, it is found that the essence behind the evolutionary law of “survival competition, survival of the fittest, survival of the fittest” in nature is an optimization idea. Evolutionary Computation (EC) is a general problem solving method developed based on this idea. It uses simple coding techniques to represent various complex structures, and through simple genetic manipulation and natural selection of survival of the fittest on a set of encoded representations, in order to guide learning and determine the direction of the search. Since it organizes the search in a population (ie, a set of coded representations), it makes it possible to search multiple regions in the solution space simultaneously [2]. And the way to organize the search with the population makes the evolutionary algorithm especially suitable for massive parallelism. While endowing evolutionary computing with features such as self-organization, self-adaptation, and self-learning, survival of the fittest by natural selection and simple genetic manipulation, make evolutionary computation unrestricted by its search space (such as emblem, continuous, unimodal, etc.) constraints and do not require other auxiliary information (such as derivatives) characteristics. These characteristics make evolutionary computing not only highly efficient, but also simple, easy to operate, and versatile.

Genetic algorithm has the following characteristics:

Self-organization, self-adaptation and self-learning (intelligence). When applying the genetic algorithm to solve the problem, after the coding scheme, fitness function and genetic operator are determined, algorithms will organize their searches on their own using the information gained during evolution. Based on the selection strategy of “survival of the fittest, and elimination of the unfit”, individuals with high fitness have a higher probability of survival. Natural selection removes one of the biggest hurdles in algorithm design, which is the need to describe all the characteristics of the problem in advance, and it should explain the measures that the algorithm should take according to the different characteristics of the problem. Therefore, the method using genetic algorithm can solve complex unstructured problems [3].

Essential parallelism. Genetic algorithms search for a population number of points in parallel, rather than a single point. Genetic algorithms have implicit parallelism. Since the genetic algorithm uses the population method to organize the search, therefore, multiple regions of the solution space can be searched at the same time, and information can be exchanged with each other. Using this search method, although only a calculation proportional to the population size N is performed each time, approximately O(N3) efficient searches have been performed in essence, this allows the genetic algorithm to obtain greater benefits with less computation.

Genetic algorithm does not need derivation or other auxiliary knowledge, but only needs the objective function and the corresponding fitness function that affects the search direction [4].

Genetic algorithms use genetic operations probabilistically instead of deterministic rules.

Robustness. Since the genetic algorithm uses the fitness of the individual to promote the evolution of the group, regardless of the structural characteristics of the problem to be solved, therefore, when solving different problems, only the corresponding fitness evaluation function needs to be designed, without modifying other parts of the algorithm, it has good robustness.

Genetic algorithm can generate many potential solutions for a given problem, and the final choice can be determined by the user. Genetic algorithms are particularly suitable for multi-objective searches or situations where alternative solution sets need to be determined.

The main applications of genetic algorithms are: Function optimization, combinatorial optimization, production scheduling problems, automatic control, intelligent robot control, image processing and pattern recognition, artificial life, genetic programming, machine learning, etc. [5].

Hassan OF et al. demonstrated the convergence of the Levenbery-Marquardtsuan (LM for short) algorithm, and Fan improved the LM algorithm and proved its convergence [6]. After the later improvement of Newton's method, many research results have appeared. Kumar S proposed the continuous Newton's method, in 2012, the multi-step Newton method was proposed, in which quadrature and variational techniques were applied to study the problem of solving nonlinear equations [7]. In order to improve the convergence of the algorithm, Qureshi U K proposed a class of BFGS-type convergence algorithms with overall and superlinear convergence, in the application of this algorithm to the solution of symmetric nonlinear equations, some scholars have been inspired by the solution of symmetric nonlinear equations, and try to use the quasi-Newton method with faster convergence speed to solve such nonlinear system of equations [8].

Based on the in-depth series of studies on nonlinear equations by predecessors, the author proposes that by embedding the QN operator in the Genetic Algorithm (GA), and define the appropriate fitness, so as to obtain a hybrid computational intelligent algorithm that combines the advantages of GA and QN method, not only has fast convergence, but also can solve CNLE with a large probability.

Newton's method is a numerical method for solving NLE in which the number of equations is consistent with the number of variables, and it has a better solution method with local square convergence. Next, the idea of Newton's method is extended to CNLE (Comenius National Library of Education), where the number of variables and the number of equations can be inconsistent.

The dimension

Expand the function _{k}_{k}_{+1} be _{k}_{+1}) = 0. Therefore, it can be seen from equation (2) that _{k}_{+1} satisfies

The number of equations of equation (3) is _{k}_{+1} may not be unique. From the theory of algebraic equations and the definition of generalized inverse matrices, the general solution of algebraic equation (3) is:

It can be seen from the above formula and formula (4) that when the number of equations of CNE is consistent with the number of variables and

Step 1 Select the initial iteration value _{0}.

Step 2 Calculate the iteration value _{1} according to the following formula.

Step 3 If _{1} makes ‖_{1})‖ ≥ ‖_{0})‖, the following correction value of _{1} is used as the new iteration value
_{1}) used in the iterative process decreases monotonically.

Step 4 If the iteration value satisfies the termination iteration condition _{1} or ‖_{1})‖ < _{2}, terminate the iteration, and take _{1} as the solution of CNLE (1), otherwise, go to step 5. Here _{1} and _{2} are allowable errors, and

Step 5 If the iteration does not reach the predetermined number of times, replace _{0} with _{1}, return to step 2 to continue the iteration, otherwise the method fails. The reason for the failure may be that the initial value is not chosen properly, or that CNLE (1) has no solution (ie, it is incompatible).

Similar to the convergence analysis of Newton's method, it can be seen that the QN method has the same local square convergence as Newton's method. Therefore, QN is a very efficient CNLE solution on a local scale, but less effective for strongly nonlinear CNLEs. For this reason, it is more meaningful to study the solution master of strong nonlinear CNLE with high solving efficiency [10].

In order to generalize the GA for global optimization to solving CNLE (8), the solving problem needs to be equivalent to the following optimization problem

The parameter _{j}

In view of the shortcomings of the QN method and GA in solving CNLE problems, and synthesizing their respective advantages, the author proposes the following HCIA Begin

Randomly generate the initial parent population and calculate its fitness

Repeat

Select two individuals in the group to perform coding hybridization and decoding operations with probability _{c}

Perform encoding, mutation and decoding operations on each individual in the group with probability _{m}

Perform the QN operator operation on each individual in the group with probability _{n}

Calculate fitness for each individual;

With a given group size, select the progeny group for the next breeding (the fittest breed, the unfit are eliminated)

Until (end iteration logic condition)

End

For the above HCIA, the description is as follows:

Since the selection probability required for hybridization and offspring selection is proportional to fitness, the definition of fitness has a global impact on GA and HCLA, which is one of the keys to the successful solution of the algorithm [11]. Fitness is defined as
_{tmax} and _{tmin} are the maximum and minimum function values of _{1} is a parameter that controls the ratio of maximum to minimum fitness. It can be seen from the above formula that the ratio of the maximum to minimum fitness in each generation is
_{1} is too large, the ratio approaches 1, that is to say, the individuals with the largest and smallest function values in the current population have relatively close fitness and selection probability, and the functions of the hybridization operator and the mutation operator will degenerate to close to a complete random search. If _{1} is too small, the ratio will approach ∞, which will make the fitness and selection probability of individuals with larger function values in the current population too small, losing the chance of reproduction, which leads to the rapid concentration of the group to one or several individuals, reduces the probability of successful solution. In general, the value of _{1} is suitable between 0.01 and 0.1, and the ratio of the maximum and minimum fitness between individuals in the same generation group is between 11 and 101.

Since the _{max} and _{min} of each generation in the algorithm change with different groups, HCIA is highly adaptive and robust in determining fitness and selection probability [12].

The main data structure of GA is a digital bit string, which is commonly used in binary. When GA is applied to solve the equation system, the length of the bit string and the encoding method have a decisive influence on the calculation accuracy and the diversity of individuals in the population, and directly affect the solution.

The data structure of HCIA adopts a hybrid data structure, and each individual in the group adopts a data structure of real numbers, only when individuals are identified for crossover and mutation operations, the binary bit string encoding in the traditional GA is carried out, after the operation, the offspring will be decoded to be added to the new offspring group. The advantage of using the hybrid data structure is that it can avoid the influence of the limited word length of the encoding on the accuracy, and give full play to the high accuracy of the QN operator and the ability to search for the solution of the equation locally and meticulously.

In order to accelerate the convergence of GA in CNLE solution, and take advantage of traditional numerical algorithms in calculation speed and accuracy, a QN operator that mainly performs one-step iterative operation in the QN method is embedded in HCLA. For the new offspring produced in each reproduction, the probability _{n}

The specific operations performed by the QN operator are:

Repeat

Generate a random number between [0, 1] for the i-th individual in the group. If the random number is greater than the predetermined QN operator probability _{n}

The downhill factor _{k}_{+1} calculated as follows, make the function

The generated offspring will replace the parent and join the new offspring group;

Until (search the entire population).

It can be said that the functions of HCIA's genetic operator - hybrid operator, mutation operator and selection operator are macro search, dealing with large-scale search problems, the function of the iterative operation process in the QN operator is local search, that is, microscopic search, which deals with small-scale search and search acceleration.

The size of the QN operator probability _{n}

Therefore, the factors to be considered in determining the value of _{n}

Iterative convergence of the QN method of the solved CNLE. If the iterative convergence is faster, the corresponding _{n}

A predetermined number of reproductions (iterations). If the predetermined breeding algebra is larger, the corresponding _{n}

Compared with the traditional numerical algorithm, the reason why GA can obtain the corresponding solution in the global scope with a large probability, it is because two basic principles are reflected in its algorithm thought: One is survival of the fittest, and the other is the relative randomness of selection. The selection operator, selection probability and controlling the distance between individuals are the most important means to embody these principles. HCIA's main considerations for this are:

After the hybridization and mutation operations, both the offspring and the parent enter the offspring candidate population at the same time. Since the QN method can guarantee that the point sequence generated by iteration is monotonically decreasing, therefore, the new individuals generated by the QN operator inherit the good qualities of the parent, so the offspring can replace the parent into the offspring candidate group, without the need for both the parent and offspring to enter the offspring candidate group.

When selecting the progeny population for next breeding, randomly select two individuals with the probability of individuals in the candidate population each time, and the individuals with large fitness enter the progeny population, until all the offspring needed for reproduction have been produced. This can not only ensure the relative survival of the fittest, but also make the selection have a certain randomness [14].

In order to avoid the rapid concentration of the group to a certain or a limited number of individuals during reproduction, reduce the probability of a successful solution, in the selection operator operation, the distance between each individual in the group must also be calculated (commonly used are 2-norm, Hamming distance, etc.), two individuals that are close to each other must be eliminated. Since the QN operator in HCIA can perform optimization searches locally and meticulously, when controlling the distance between individuals in a group, it can be considered to make the relative distance between individuals larger (generally, the relative error can be more than 10%), it enables the solution to be successful with a greater probability in a larger spatial range.

This section discusses the solution of the following three equations in the specified interval.

The author uses the QN method and HCIA proposed above to carry out numerical calculation, and the weighting coefficient _{j}^{−6}, it is considered that the solution is found and the algorithm is successful; For example 2 and example 3, if ^{−5}, the search is considered successful. The calculation results are shown in Table 1 and Table 2.

Calculation results of Example 1

Quasi-Newton method_{c}_{m}_{n} |
Hybrid Computational Intelligence Algorithm_{c}_{m} |
||||||||
---|---|---|---|---|---|---|---|---|---|

_{n} |
0.005 | 0.01 | 0.025 | 0.05 | 0.075 | 0.1 | 0.2 | ||

Number and probability of finding a solution | 60 |
46 |
60 |
60 |
60 |
60 |
60 |
60 |
60 |

reproductive algebra | 2500 | 10000 | 2500 | 2500 | 2500 | 2500 | 2500 | 2500 | 2500 |

Calculation results of Example 2 and Example 3

Example 2 | Example 3 | reproductive algebra | ||
---|---|---|---|---|

Number and probability of finding a solution | Number and probability of finding a solution | |||

Quasi-Newton method_{c}_{m}_{n} |
4 |
3 |
2500 | |

Hybrid Computational Intelligence Algorithm_{c}_{m} |
_{n} |
6 |
6 |
2500 |

0.25 | 17 |
20 |
2500 | |

0.50 | 21 |
31 |
2500 | |

0.75 | 31 |
33 |
2500 | |

0.1 | 39 |
36 |
2500 | |

0.15 | 45 |
52 |
2500 | |

0.2 | 48 |
50 |
2500 | |

0.3 | 60 |
60 |
2500 | |

0.4 | 60 |
60 |
2500 | |

0.5 | 60 |
60 |
2500 |

The above calculation results are explained and analyzed as follows:

When _{c}_{m}_{n}_{i}

When _{n}

The HCIA proposed by the author, which combines the specialties of GA and QN method, can give full play to the genetic operator and mutation operator to search for global solutions in a large range, and the characteristic of QN operator in local and meticulous search, for CNLE composed of functions similar to Example 2 and Example 3, which are non-monotonic and have multiple local extreme points, the probability of finding a solution is significantly higher than that of the QN method and GA; For CNLE composed of monotonic functions similar to Example 1, the probability of obtaining a solution is equivalent to that of the QN method. The value of the selection probability _{n}_{n}_{n}_{n}_{n}

From the above calculation results, it can be seen that, the HCLA proposed by the author based on GA and QN method, the probability of obtaining a solution in the specified space is significantly greater than that of QN method and GA, and it is a feasible numerical algorithm for CNLE [16].

The author combines the special HCIA of GA and Newton's method, which can give full play to the characteristics of genetic operators in large-scale search for global solutions, and the characteristic of Newton operator in local and meticulous search, for the nonlinear equation system composed of non-monotonic multimodal functions similar to Example 2, the probability of obtaining the solution is significantly higher than that of Newton's method and GA; For the nonlinear system of equations composed of monotonic functions similar to those in Example 1, the probability of obtaining a solution is equivalent to that of Newton's method. The size of the selection probability of the Newton operator also directly affects the solution efficiency. Generally speaking, can be larger for strong nonlinear equations composed of multimodal functions; can be smaller for weak nonlinear equations composed of functions with few extreme points and strong monotonicity.

#### Calculation results of Example 2 and Example 3

reproductive algebra | ||||
---|---|---|---|---|

Number and probability of finding a solution | Number and probability of finding a solution | |||

Quasi-Newton method_{c}_{m}_{n} |
4 |
3 |
2500 | |

Hybrid Computational Intelligence Algorithm_{c}_{m} |
_{n} |
6 |
6 |
2500 |

0.25 | 17 |
20 |
2500 | |

0.50 | 21 |
31 |
2500 | |

0.75 | 31 |
33 |
2500 | |

0.1 | 39 |
36 |
2500 | |

0.15 | 45 |
52 |
2500 | |

0.2 | 48 |
50 |
2500 | |

0.3 | 60 |
60 |
2500 | |

0.4 | 60 |
60 |
2500 | |

0.5 | 60 |
60 |
2500 |

#### Calculation results of Example 1

Quasi-Newton method_{c}_{m}_{n} |
Hybrid Computational Intelligence Algorithm_{c}_{m} |
||||||||
---|---|---|---|---|---|---|---|---|---|

_{n} |
0.005 | 0.01 | 0.025 | 0.05 | 0.075 | 0.1 | 0.2 | ||

Number and probability of finding a solution | 60 |
46 |
60 |
60 |
60 |
60 |
60 |
60 |
60 |

reproductive algebra | 2500 | 10000 | 2500 | 2500 | 2500 | 2500 | 2500 | 2500 | 2500 |

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Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities 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Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on 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Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model