Preconditioners based on the ISM factorization ∗
نویسندگان
چکیده
In this paper we survey our work on preconditioners based on the Inverse Sherman-Morrison factorization. The most important theoretical results are also summarized and some numerical conclusions are provided.
منابع مشابه
ILU and IUL factorizations obtained from forward and backward factored approximate inverse algorithms
In this paper, an efficient dropping criterion has been used to compute the IUL factorization obtained from Backward Factored APproximate INVerse (BFAPINV) and ILU factorization obtained from Forward Factored APproximate INVerse (FFAPINV) algorithms. We use different drop tolerance parameters to compute the preconditioners. To study the effect of such a dropping on the quality of the ILU ...
متن کاملParallel Triangular Solvers on GPU
In this paper, we investigate GPU based parallel triangular solvers systematically. The parallel triangular solvers are fundamental to incomplete LU factorization family preconditioners and algebraic multigrid solvers. We develop a new matrix format suitable for GPU devices. Parallel lower triangular solvers and upper triangular solvers are developed for this new data structure. With these solv...
متن کاملModified Incomplete Cholesky Factorization Preconditioners for a Symmetric Positive Definite Matrix
We propose variants of the modified incomplete Cholesky factorization preconditioner for a symmetric positive definite (SPD) matrix. Spectral properties of these preconditioners are discussed, and then numerical results of the preconditioned CG (PCG) method using these preconditioners are provided to see the effectiveness of the preconditioners.
متن کاملFactorization-based Sparse Solvers and Preconditioners
Efficient solution of large-scale, ill-conditioned and highly-indefinite algebraic equations often relies on high quality preconditioners together with iterative solvers. Because of their robustness, factorizationbased algorithms play a significant role in developing scalable solvers. We discuss the state-of-the-art, high performance sparse factorization techniques which are used to build spars...
متن کاملIncomplete Cholesky Factorization with Sparsity Pattern Modi cation
This paper proposes, analyzes, and numerically tests methods to assure the existence of incomplete Cholesky (IC) factorization preconditioners, based solely on the target sparsity pattern for the triangular factor R. If the sparsity pattern has a simple property (called property C+), then the IC factor exists in exact arithmetic. Two algorithms for modifying the target sparsity pattern to have ...
متن کامل