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Conditioning analysis of positive definite matrices by approximate factorizations. (English) Zbl 0678.65029

The conditioning analysis of positive definite matrices by approximate LU factorizations is usually reduced to that of Stieltjes matrices by means of perturbation arguments like spectral equivalence. The authors define “almost Stieltjes” matrices \(A:=A_ 0+A_ 2,\) where \(A_ 0\) is a Stieltjes matrix while \(A_ 2\) is both nonnegative and nonnegative definite. They show that this class of matrices can be used as a reference class for the conditioning analysis. This is advantageous especially for the conditioning analysis of finite element approximations of large multidimensional steady-state diffusion problems.
Reviewer: N.K√∂ckler

MSC:

65F35 Numerical computation of matrix norms, conditioning, scaling
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations

Software:

symrcm
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References:

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