Rational Krylov for Stieltjes matrix functions: convergence and pole selection

• Published in: BIT Vol. 61; no. 1; pp. 237 - 273
• Main Authors: Massei, Stefano, Robol, Leonardo
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.03.2021; Springer Nature B.V
• Subjects: Approximation; Computational Mathematics and Numerical Analysis; Convergence; Error analysis; Mathematical analysis; Mathematics; Mathematics and Statistics; Matrix methods; Numeric Computing; Subspaces; Tensors; Zolotarev problem; 65F60; 30E20; Pole selection; Rational Krylov; Function of matrices; 65E05; Kronecker sum; Stieltjes functions

Evaluating the action of a matrix function on a vector, that is  x = f ( M ) v , is an ubiquitous task in applications. When  M  is large, one usually relies on Krylov projection methods. In this paper, we provide effective choices for the poles of the rational Krylov method for approximating  x  wh...