The Lanczos algorithm for matrix functions: a handbook for scientists

Understand

Lanczos-based methods have become standard tools for tasks involving matrix functions.

• Progress on these algorithms has been driven by several largely disjoint communities, resulting many innovative and important advancements which would not have been possible otherwise.
• However, this also has resulted in a somewhat fragmented state of knowledge and the propagation of a number of incorrect beliefs about the behavior of Lanczos-based methods in finite precision arithmetic.
• This monograph aims to provide an accessible introduction to Lanczos-based methods for matrix functions.