Extended nonsymmetric global Lanczos method for matrix function approximation

Extended Krylov subspace methods are attractive methods for computing approximations of matrix functions and other problems producing large-scale matrices. In this work, we propose the extended nonsymmetric global Lanczos method for solving some matrix approximation problems. The derived algorithm uses short recursive relations to generate bi-orthonormal bases, with respect to the Frobenius inner product, of the corresponding extended Krylov subspacesKme(A,V) are two blocks. New algebraic properties of the proposed method are developed and applications to approximation of bothW(T)f(A)Vand trace(W(T)f(A)V) are given. Numerical examples are presented to show the performance of the extended nonsymmetric global Lanczos for these problems.