Shift-Invert Arnoldi Approximation to the Toeplitz Matrix Exponential

The shift-invert Arnoldi method is employed to generate an orthonormal basis from the Krylov subspace corresponding to a real Toeplitz matrix and an initial vector. The vectors and recurrence coefficients produced by this method are exploited to approximate the Toeplitz matrix exponential. Toeplitz matrix inversion formula and rapid Toeplitz matrix-vector multiplications are utilized to lower the computational costs. For convergence analysis, a sufficient condition is established to guarantee that the error bound is independent of the norm of the matrix. Numerical results are given to demonstrate the efficiency of the method. Key words. Toeplitz matrix, matrix exponential, Krylov subspace, shift-invert Arnoldi method, numerical range AMS subject classifications. 65L05, 65N22, 65F10, 65F15 DOI. 10.1137/090758064

• Type: Journal
• Year: 2010
• Where: SIAMSC
• Authors: Spike T. Lee, Hong-Kui Pang, Hai-Wei Sun
• Keywords: Matrix Exponential, Shift-invert Arnoldi Method, SIAMSC 2010, Toeplitz Matrix