A generalized isometric Arnoldi algorithm (Q880025)

Suppose \(A\) is an isometry on a Hilbert space. The author shows that the isometric Arnoldi algorithm yields a sequence of matrices \(M_{j}\) and can be interpreted as a structured form of a modified Gram-Schmidt process. The algorithm is described in terms of projections and inner products. Numerical experiments suggest that compared to a generalized Schur algorithm, the new one improves the numerical orthogonality of the sequence. Contents: Introduction; A general form of the isometric Arnoldi algorithm; Krylov-like sequences; Orthogonality relations; The factored algorithm; Computing QR factorization; Preliminary numerical experiments; Additional topics.