A symmetric band Lanczos process based on coupled recurrences and some applications (Q2780539)

The authors propose a new variant of the band Lanczos process for symmetric matrices and multiple starting vectors. In the standard version an \(n \times n\) projection \(T_n^s\) of the given symmetric matrix onto the \(n\)-dimensional subspace spanned by the first \(n\) Lanczos vectors is computed directly. In the new version coupled recurrences involving two sets of basis vectors are used to produce the factors of an \(LDL^T\) factorization of an \(n \times n\) matrix \(T_n\) which is closely related to \(T_n^s\). NEWLINENEWLINENEWLINEApplications of the proposed method to reduced-order modeling of large electronic circuits and to generalised symmetric eigenvalue problems are discussed and numerical examples are presented. The numerical results show that the new variant is more robust and accurate than the standard version.