A QR-decomposition of block tridiagonal matrices generated by the block Lanczos process
نویسندگان
چکیده
For MinRes and SymmLQ it is essential to compute a QR decomposition of a tridiagonal coefficient matrix gained in the Lanczos process. This QR decomposition is constructed by an update scheme applying in every step a single Givens rotation. Using complex Householder reflections we generalize this idea to block tridiagonal matrices that occur in generalizations of MinRes and SymmLQ to block methods for systems with multiple right-hand sides. Some implementation details are given, and we compare the method with an algorithm based on Givens rotations used in block QMR. Our approach generalizes to the QR decomposition of upper block Hessenberg matrices resulting from the block Arnoldi process and is applicable in block GMRes. Keywords— block Lanczos process, block Krylov space methods. I. The symmetric Lanczos algorithm In 1975 Christopher Paige and Michael Saunders [PAI 75] proposed two iterative Krylov subspace methods called MinRes and SymmLQ for solving sparse Hermitian indefinite linear systems
منابع مشابه
Updating the QR decomposition of block tridiagonal and block Hessenberg matrices generated by block Krylov space methods
For MinRes and SymmLQ it is essential to compute the QR decompositions of tridiagonal coefficient matrices gained in the Lanczos process. Likewise, for GMRes one has to find those of Hessenberg matrices. These QR decompositions are computed by an update scheme where in every step a single Givens rotation is constructed. Generalizing this approach we introduce a block-wise update scheme for the ...
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