Local fill reduction techniques for sparse symmetric linear systems
نویسنده
چکیده
Local algorithms for obtaining pivot orderings for sparse symmetric coefficient matrices are reviewed together with their mathematical background, appropriate data structures and details of efficient implementation. Heuristics that go beyond the classical Minimum Degree and Minimum Local Fill scoring functions are discussed, illustrated, improved and extensively tested on a test suite of matrices from various applications. Our tests indicate that the presented techniques have the potential of accelerating circuit simulation significantly.
منابع مشابه
"Compress and eliminate" solver for symmetric positive definite sparse matrices
We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in. The systems that have efficient compression of the fill-in mostly arise from discretization of partial differential equations. We show that the resulting fa...
متن کاملSymbolic Factorisation of Sparse Matrix Using Elimination Trees
Many problems in science and engineering require the solving of linear systems of equations. As the problems get larger it becomes increasingly important to exploit the sparsity inherent in many such linear systems. It is well recognized that finding a fill-reducing ordering is crucial to the success of the numerical solution of sparse linear systems. The use of hybrid ordering partitioner is e...
متن کاملPreconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation
Introduction Fractional differential equations (FDEs) have attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme may be a good approach, particularly, the schemes in numerical linear algebra for solving ...
متن کاملOn methods for ordering sparse matrices in circuit simulation
Recently proposed methods for ordering sparse symmetric matrices are discussed and their performance is compared with that of the Minimum Degree and the Minimum Local Fill algorithms. It is shown that these methods applied to symmetrized modified nodal analysis matrices yield orderings significantly better than those obtained from the Minimum Degree and Minimum Local Fill algorithms, in some ca...
متن کاملMinimum Degree Reordering Algorithms: A Tutorial
The problem of matrix inversion is central to many applications of Numerical Linear Algebra. When the matrix to invert is dense, little can be done to avoid the costly O(n) process of Gaussian Elimination. When the matrix is symmetric, one can use the Cholesky Factorization to reduce the work of inversion (still O(n), but with a smaller coefficient). When the matrix is both sparse and symmetric...
متن کامل