Searching for authors named "Thomas Huckle" – sorted by Relevance.
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Implementation of a Superfast Algorithm for Symmetric Positive Definite Linear Equations of Displacement Rank 2
- …In this paper we describe the implementation and first numerical results for the superfast algorithm based on a modified version of the Bitmead/Anderson-algorithm for real symmetric positive definite matrices of displacement rank 2. The total number of arithmetic operations for this algorithm is of …
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Sparse Approximate Inverses for Preconditioning of Linear Equations
- …onditioners, or incomplete LU-decompositions of A [2]. But these preconditioners either lead to unsatisfactorily convergence or are hard to parallelize. A very promising approach is the choice of sparse approximate inverses for preconditioning, M ß A \Gamma1 and M sparse [10,4,3,7,6,8]. Then, in t…
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Multigrid Preconditioning and Toeplitz Matrices
- …In this paper we discuss Multigrid methods for Toeplitz matrices. Then the restriction and prolongation operator can be seen as projected Toeplitz matrices. Because of the intimate connection between such matrices and trigonometric series we can express the Multigrid algorithm in terms of the underl…
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PVM-Implementation of Sparse Approximate Inverse Preconditioners for Solving Large Sparse Linear Equations
- …to convergent iterates if the spectral radius ae(M \Gamma1 K) ! 1. For many important iterative methods the convergence depends heavily on the position of the eigenvalues of A. Therefore, the original system Ax = b is often replaced by an equivalent system MAx = Mb or the system AMz = b, x = Mz . …
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Computation of Gohberg-Semencul Formulas for a Toeplitz Matrix
- …The inverse of a Toeplitz matrix can be represented in different ways by Gohberg-Semencul formulas as the sum of products of upper and lower triangular Toeplitz matrices. If we have given such a Gohberg-Semencul formula we can solve every equation Tnx = b in O(n log(n)) steps. But we have to decide…
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Iterative methods for ill-conditioned Toeplitz Matrices
- …. In this paper we study the use of the Sine Transform for preconditioning linear Toeplitz systems. We consider Toeplitz matrices with a real generating function that is nonnegative with only a small number of zeros. Then we can define a preconditioner of the form S n S n where S n is the matrix des…
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Iterative Methods for Toeplitz-like Matrices
- …. In this paper we will give a survey on iterative methods for solving linear equations with Toeplitz matrices. We introduce a new class of Toeplitz matrices for which clustering of eigenvalues and singular values can be proved. We consider optimal (!)- circulant preconditioners as a generalization …
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Superfast Solution of Linear Equations with Low Displacement Rank
- …For the solution of linear equations with symmetric positive definite Toeplitz matrices there exist the classical fast solvers with O(n 2 ) operations, and the superfast solvers with O(n lg(n) 2 ). Superfast algorithms with a large constant c in O(n lg(n) 2 ) are not interesting because they …
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A New Approach to Parallel Preconditioning with Sparse Approximate Inverses
- …A new parallel preconditioner is presented for the solution of large, sparse, nonsymmetric linear systems of equations. A sparse approximate inverse is computed explicitly, and then applied as a preconditioner to an iterative method. The computation of the preconditioner is inherently parallel, and …
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Multigrid Preconditioning and Toeplitz Matrices
- …In this paper we discuss Multigrid methods for Toeplitz matrices. Then the restriction and prolongation operator can be seen as projected Toeplitz matrices. Because of the intimate connection between such matrices and trigonometric series we can express the Multigrid algorithm in terms of the underl…
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