On Krylov Subspace Approximations to the Matrix Exponential Operator
نویسندگان
چکیده
منابع مشابه
Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
In this note we present a theoretical analysis of some Krylov subspace approximations to the matrix exponential operation exp(A)v and establish a priori and a posteriori error estimates. Several such approximations are considered. The main idea of these techniques is to approximately project the exponential operator onto a small Krylov subspace and carry out the resulting small exponential matr...
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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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Matrix exponential discriminant analysis (EDA) is a generalized discriminant analysis method based on matrix exponential. It can essentially overcome the intrinsic difficulty of small sample size problem that exists in the classical linear discriminant analysis (LDA). However, for data with high dimension, one has to solve a large matrix exponential eigenproblem in this method, and the time com...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 1997
ISSN: 0036-1429,1095-7170
DOI: 10.1137/s0036142995280572