The Snap-Back Pivoting Method for Symmetric Banded Indefinite Matrices
نویسندگان
چکیده
منابع مشابه
The Snap-Back Pivoting Method for Symmetric Banded Indefinite Matrices
The four existing stable factorization methods for symmetric indefinite pivoting (row or column exchanges) maintains a band structure in the reduced matrix and the factors, but destroys symmetry completely once an off-diagonal pivot is used. Two-by-two block pivoting maintains symmetry at all times, but quickly destroys the band structure. Gaussian reduction to tridiagonal also maintains symmet...
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We consider ways of implementing preordering and scaling for symmetric systems and show the effect of using this technique with a multifrontal code for sparse symmetric indefinite systems. After having presented a new method for scaling, we propose a way of using an approximation to a symmetric weighted matching to predefine 1×1 and 2×2 pivots prior to the ordering and analysis phase. We also p...
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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: SIAM Journal on Matrix Analysis and Applications
سال: 2006
ISSN: 0895-4798,1095-7162
DOI: 10.1137/040610106