In this paper, an algorithm based on a shifted inverse power iteration for computing generalized eigenvalues with corresponding eigenvectors of a large scale sparse symmetric positive definite matrix pencil is present...In this paper, an algorithm based on a shifted inverse power iteration for computing generalized eigenvalues with corresponding eigenvectors of a large scale sparse symmetric positive definite matrix pencil is presented. It converges globally with a cubic asymptotic convergence rate, preserves sparsity of the original matrices and is fully parallelizable. The algebraic multilevel itera-tion method (AMLI) is used to improve the efficiency when symmetric positive definite linear equa-tions need to be solved.展开更多
In this paper, an algorithm for computing some of the largest (smallest) generalized eigenvalues with corresponding eigenvectors of a sparse symmetric positive definite matrix pencil is presented. The algorithm uses a...In this paper, an algorithm for computing some of the largest (smallest) generalized eigenvalues with corresponding eigenvectors of a sparse symmetric positive definite matrix pencil is presented. The algorithm uses an iteration function and inverse power iteration process to get the largest one first, then executes m - 1 Lanczos-like steps to get initial approximations of the next m - 1 ones, without computing any Ritz pair, for which a procedure combining Rayleigh quotient iteration with shifted inverse power iteration is used to obtain more accurate eigenvalues and eigenvectors. This algorithm keep the advantages of preserving sparsity of the original matrices as in Lanczos method and RQI and converges with a higher rate than the method described in [12] and provides a simple technique to compute initial approximate pairs which are guaranteed to converge to the wanted m largest eigenpairs using RQL. In addition, it avoids some of the disadvantages of Lanczos and RQI, for solving extreme eigenproblems. When symmetric positive definite lira ear systems must be solved in the process, an algebraic multilevel iteration method (AMLI) is: applied. The algorithm is fully parallelizable. [ABSTRACT FROM AUTHOR]展开更多
文摘In this paper, an algorithm based on a shifted inverse power iteration for computing generalized eigenvalues with corresponding eigenvectors of a large scale sparse symmetric positive definite matrix pencil is presented. It converges globally with a cubic asymptotic convergence rate, preserves sparsity of the original matrices and is fully parallelizable. The algebraic multilevel itera-tion method (AMLI) is used to improve the efficiency when symmetric positive definite linear equa-tions need to be solved.
文摘In this paper, an algorithm for computing some of the largest (smallest) generalized eigenvalues with corresponding eigenvectors of a sparse symmetric positive definite matrix pencil is presented. The algorithm uses an iteration function and inverse power iteration process to get the largest one first, then executes m - 1 Lanczos-like steps to get initial approximations of the next m - 1 ones, without computing any Ritz pair, for which a procedure combining Rayleigh quotient iteration with shifted inverse power iteration is used to obtain more accurate eigenvalues and eigenvectors. This algorithm keep the advantages of preserving sparsity of the original matrices as in Lanczos method and RQI and converges with a higher rate than the method described in [12] and provides a simple technique to compute initial approximate pairs which are guaranteed to converge to the wanted m largest eigenpairs using RQL. In addition, it avoids some of the disadvantages of Lanczos and RQI, for solving extreme eigenproblems. When symmetric positive definite lira ear systems must be solved in the process, an algebraic multilevel iteration method (AMLI) is: applied. The algorithm is fully parallelizable. [ABSTRACT FROM AUTHOR]
