Preconditioning Lanczos Approximations to the Matrix Exponential
نویسندگان
چکیده
منابع مشابه
Preconditioning Lanczos Approximations to the Matrix Exponential
The Lanczos method is an iterative procedure to compute an orthogonal basis for the Krylov subspace generated by a symmetric matrix A and a starting vector v. An interesting application of this method is the computation of the matrix exponential exp(−τA)v. This vector plays an important role in the solution of parabolic equations where A results from some form of discretization of an elliptic o...
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When A is a Hermitian matrix, the action f(A)b of a matrix function f(A) on a vector b can efficiently be approximated via the Lanczos method. In this note we use M -matrix theory to establish that the 2norm of the error of the sequence of approximations is monotonically decreasing if f is a Stieltjes transform and A is positive definite. We discuss the relation of our approach to a recent, mor...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2006
ISSN: 1064-8275,1095-7197
DOI: 10.1137/040605461