Work

Unified Newton’s method for matrix decompositions

Year: 2026

Type: article

Abstract: We propose a way to unify the construction of Newton’s methods for matrix decompositions. This construction is based on a perturbation analysis of a suitable system associated with matrix decompositions. Then it appears that the resolution of a linear Sylvester equation permits defining Newton’s method. We give a general result to analyze the quadratic convergence of this Newton’s method. We apply it to classical matrix decompositions: LU decomposition, QR decomposition, eigenproblem in the diagonalizable case, singular value decomposition, and Schur decomposition. Finally, we propose for future work a generalization of this construction to approximate matrix decomposition by high-order methods.

Source: Applicable Algebra in Engineering Communication and Computing

DOI: 10.1007/s00200-025-00720-7

Author: Jean-Claude Yakoubsohn

Institutions: Université Toulouse III - Paul Sabatier, Institut de Mathématiques de Toulouse

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Université de Toulouse