Limited-memory polynomial methods for large-scale matrix functions

Abstrakt

Matrix functions are a central topic of linear algebra, and problems requiring their numerical approximation appear increasingly often in scientific computing. We review various limited-memory methods for the approximation of the action of a large-scale matrix function on a vector.

Emphasis is put on polynomial methods, whose memory requirements are known or prescribed a priori. Methods based on explicit polynomial approximation or interpolation, as well as restarted Arnoldi methods, are treated in detail.

An overview of existing software is also given, as well as a discussion of challenging open problems.

Klíčová slova

• Krylovov method
• limited memory
• matrix function
• polynomial approximation
• restarting