An NPDo Approach for Principal Joint SVD-type Block Diagonalization

TL;DR

This paper introduces an NPDo approach for Principal Joint SVD-type Block Diagonalization, optimizing the collective dominant block-diagonal parts of multiple matrices with proven convergence and demonstrated efficiency.

Contribution

The paper proposes a novel NPDo method combined with Gauss-Seidel updating for joint block diagonalization, ensuring global convergence and improved optimization.

Findings

NPDo approach effectively maximizes common dominant block-diagonal parts.

The method guarantees convergence to a stationary point.

Numerical experiments confirm the approach's efficiency.

Abstract

This paper is concerned with partial Joint SVD-type Block Diagonalization of several matrices so that the extracted diagonal parts collectively optimally assume part of the total mass of all given matrices. For that reason, it will be referred also as Principal Joint SVD-type Block Diagonalization. When each block-size is 1-by-1, it is about finding a dominant partial joint SVD decomposition for the matrices of interests. An NPDo approach is proposed for maximizing the common dominant block-diagonal parts collectively. It is shown that the NPDo approach combined with Gauss-Seidel-type updating is globally convergent to a stationary point while the objective increases monotonically. Numerical experiments are presented to illustrate the efficiency of the NPDo approach.