Symmetric elimination without pivoting
نویسندگان
چکیده
منابع مشابه
Probabilistic Analysis of Complex Gaussian Elimination without Pivoting
We consider Gaussian elimination without pivoting applied to complex Gaussian matrices X ∈ Cn×n. We first study some independence properties of the elements of the LU factors of X. Based on this, we then derive the probability distributions for all the L and U elements and obtain bounds for the probabilities of the occurrence of small pivots and large growth factors. Numerical experiments are p...
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Recently codes have been developed for computing the Cholesky factorization with complete pivoting of a symmetric positive semidefinite matrix for the serial LAPACK library. In the parallel ScaLAPACK library there are only routines for the unpivoted factorization in the positive definite case and no algorithms use complete pivoting. We aim to assess the feasibility of complete pivoting in ScaLA...
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Gaussian elimination with partial pivoting is performed routinely, millions times per day around the world, but partial pivoting (that is, row interchange of an input matrix) is communication intensive and has become the bottleneck of the elimination algorithm in the present day computer environment, in both cases of matrices of large and small size. Gaussian elimination with no pivoting as wel...
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The LBL factorization of Bunch for solving linear systems involving a symmetric indefinite tridiagonal matrix T is a stable, efficient method. It computes a unit lower triangular matrix L and a block 1×1 and 2×2 matrix B such that T = LBL . Choosing the pivot size requires knowing a priori the largest element σ of T in magnitude. In some applications, it is required to factor T as it is formed ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2014
ISSN: 0024-3795
DOI: 10.1016/j.laa.2014.03.026