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Journal Articles Journal of Scientific Computing Year : 2022

An Extended-Rational Arnoldi Method for Large Matrix Exponential Evaluations

A. Bentbib
  • Function : Author
M. El Ghomari
  • Function : Author

Abstract

The numerical computation of a matrix function such as exp (−t A)V , where A is an n × n large and sparse matrix, V is an n × p block with p n, and t > 0 arises in various applications including network analysis, the solution of time-dependent partial differential equations (PDE’s) and others. In this work, we propose the use of the global extended- rational Arnoldi method for computing approximations of such functions. The derived method projects the initial problem onto the global extended-rational Krylov subspace RKe m (A, V ) = span{∏m i=1(A + si I n )−1 V , . . . , (A + s1 I n )−1 V , V , AV , . . . , A m−1 V } of a low dimension. An adaptive procedure of getting the shifts {s1, . . . , sm } during the algorithmic process is given and analyzed. Applications to the solution of time-dependent PDE’s and to network analysis are presented. Numerical examples are presented to show the performance of the global extended-rational Arnoldi process
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Dates and versions

hal-04413474 , version 1 (23-01-2024)

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A. Bentbib, M. El Ghomari, Khalide Jbilou. An Extended-Rational Arnoldi Method for Large Matrix Exponential Evaluations. Journal of Scientific Computing, 2022, 91, pp.36. ⟨10.1007/s10915-022-01808-9⟩. ⟨hal-04413474⟩
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