Error Bounds for the Lanczos Methods for Approximating Matrix Exponentials
نویسندگان
چکیده
منابع مشابه
Error Bounds for the Lanczos Methods for Approximating Matrix Exponentials
In this paper, we present new error bounds for the Lanczos method and the shift-andinvert Lanczos method for computing e−τAv for a large sparse symmetric positive semidefinite matrix A. Compared with the existing error analysis for these methods, our bounds relate the convergence to the condition numbers of the matrix that generates the Krylov subspace. In particular, we show that the Lanczos m...
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Having good estimates or even bounds for the error in computing approximations to expressions of the form f(A)v is very important in practical applications. In this paper we consider the case that A is Hermitian and that f is a rational function. We assume that the Lanczos method is used to compute approximations for f(A)v and we show how to obtain a posteriori upper and lower bounds on the `2-...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2013
ISSN: 0036-1429,1095-7170
DOI: 10.1137/11085935x