<abstract xmlns="http://www.w3.org/1999/xhtml"> We present in this paper a new method to determine the k largest singular values and their corresponding singular vectors for real rectangular matrices A ∈ Rn×m. Our approach is based on using a block version of the Power Method to compute an k-block SV D decomposition: Ak = Uk∑kVkT , where ∑k is a diagonal matrix with the k largest non-negative, monotonically decreasing diagonal σ1≥ σ2 ⋯ ≥ σk. Uk and Vk are orthogonal matrices whose columns are the left and right singular vectors of the k largest singular values. This approach is more efficient as there is no need of calculation of all singular values. The QR method is also presented to obtain the SV D decomposition.</abstract>

We present in this paper a new method to determine the k largest singular values and their corresponding singular vectors for real rectangular matrices A ∈ Rn×m. Our approach is based on using a block version of the Power Method to compute an k-block SV D decomposition: Ak = Uk∑kVkT , where ∑k is a diagonal matrix with the k largest non-negative, monotonically decreasing diagonal σ1≥ σ2 ⋯ ≥ σk. Uk and Vk are orthogonal matrices whose columns are the left and right singular vectors of the k largest singular values. This approach is more efficient as there is no need of calculation of all singular values. The QR method is also presented to obtain the SV D decomposition.

Block Power Method for SVD Decomposition

Department of Mathematics, Laboratoire LAMAI Facultés des Sciences et Techniques-Guéliz, BP 549 Marrakech,

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Block Power Method for SVD Decomposition"}

We present in this paper a new method to determine the k largest singular values and their corresponding singular vectors for real rectangular matrices A ∈...

Block Power Method for SVD Decomposition

Published Online: Apr 22, 2017

Page range: 45 - 58

Received: Nov 01, 2013

Accepted: Jun 01, 2014

DOI: https://doi.org/10.1515/auom-2015-0024

Keywords
Eigenvalues, Power Method, Singular, values

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Block Power Method for SVD Decomposition

Published Online: Apr 22, 2017

Page range: 45 - 58

Received: Nov 01, 2013

Accepted: Jun 01, 2014

DOI: https://doi.org/10.1515/auom-2015-0024

KeywordsEigenvalues, Power Method, Singular, values

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Eigenvalues, Power Method, Singular, values