Using Krylov approximations to the matrix exponential operator in Davidson's method

✍ Scribed by Karl Meerbergen; Miloud Sadkane

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 197 KB
• Volume: 31
• Category: Article
• ISSN: 0168-9274
• DOI: 10.1016/s0168-9274(98)00134-2

✦ Synopsis

This paper presents a new look at Davidson's method for the calculation of the rightmost eigenvalue(s). The combination of time-stepping by the Krylov exponential propagator and the Davidson method leads to a method that builds a Krylov space of the matrix exponential. The method is well-suited when only a matrix-vector multiplication by A is possible. The paper presents some convergence results and numerical examples, including a comparison with the Jacobi-Davidson method.