TY - JOUR

T1 - Preconditioning the matrix exponential operator with applications

AU - Castillo, Paul

AU - Saad, Yousef

PY - 1998/9/1

Y1 - 1998/9/1

N2 - The idea of preconditioning is usually associated with solution techniques for solving linear systems or eigenvalue problems. It refers to a general method by which the original system is transformed into one which admits the same solution but which is easier to solve. Following this principle we consider in this paper techniques for preconditioning the matrix exponential operator, e Ay 0, using different approximations of the matrix A. These techniques are based on using generalized Kunge Kutta type methods. Preconditioned based on the sparsity structure of the matrix, such as diagonal, block diagonal, and least-squares tensor sum approximations arc presented. Numerical experiments are reported to compare the quality of the schemes introduced.

AB - The idea of preconditioning is usually associated with solution techniques for solving linear systems or eigenvalue problems. It refers to a general method by which the original system is transformed into one which admits the same solution but which is easier to solve. Following this principle we consider in this paper techniques for preconditioning the matrix exponential operator, e Ay 0, using different approximations of the matrix A. These techniques are based on using generalized Kunge Kutta type methods. Preconditioned based on the sparsity structure of the matrix, such as diagonal, block diagonal, and least-squares tensor sum approximations arc presented. Numerical experiments are reported to compare the quality of the schemes introduced.

KW - Exponential operator

KW - Generalized Runge Kutta methods

KW - Preconditioner

UR - http://www.scopus.com/inward/record.url?scp=0032154341&partnerID=8YFLogxK

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U2 - 10.1023/A:1023219016301

DO - 10.1023/A:1023219016301

M3 - Article

AN - SCOPUS:0032154341

VL - 13

SP - 275

EP - 302

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

SN - 0885-7474

IS - 3

ER -