Year: 2026
Type: article
Abstract: This paper presents some theoretical results relating the Bregman log determinant matrix divergence to Kaporin's condition number. These can be viewed as nearness measures between a preconditioner and a given matrix, and we show under which conditions these two functions coincide. We also give examples of constraint sets over which it is equivalent to minimize these two objectives. We focus on preconditioners that are the sum of a positive definite and low-rank matrix, which were developed in a previous work. These were constructed as minimizers of the aforementioned divergence, and we show that they are only a constant scaling from also minimizingKaporin's condition number. We highlight connections to information geometry and comment on future directions.
Authors: Andreas A. Bock, Martin S. Andersen
Institution: Technical University of Denmark
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Funder: Novo Nordisk
Award: G412269763
OpenAlex ID: W4416423100
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