Error Estimates and Evaluation of Matrix Functions via the Faber Transform
SIAM Journal on Numerical Analysis2009Vol. 47(5), pp. 3849–3883
Citations Over TimeTop 1% of 2009 papers
Abstract
The need to evaluate expressions of the form $f(A)$ or $f(A)b$, where f is a nonlinear function, A is a large sparse $n\times n$ matrix, and b is an n-vector, arises in many applications. This paper describes how the Faber transform applied to the field of values of A can be used to determine improved error bounds for popular polynomial approximation methods based on the Arnoldi process. Applications of the Faber transform to rational approximation methods and, in particular, to the rational Arnoldi process also are discussed.
Related Papers
- → Regions of meromorphy determined by the degree of best rational approximation(1971)24 cited
- → Generalizations of σ–field and new collections of sets noted by δ–field(2019)12 cited
- → On α–field and β–field(2019)7 cited
- → Study on the Rational Function Characterization of Wide-Angle AVO(2018)
- → RATIONAL FUNCTIONS(1973)