6533b829fe1ef96bd128af4b

RESEARCH PRODUCT

Qualitative analysis of matrix splitting methods

P. TarvainenI. Faragó

subject

Pure mathematicsSOR methodTridiagonal matrixLinear systemBlock (permutation group theory)Tridiagonal matrix algorithmDomain decomposition methodsComputer Science::Numerical AnalysisStieltjes-Toeplitz matricesMathematics::Numerical AnalysisAlgebraComputational MathematicsQualitative analysisComputational Theory and MathematicsMatrix splittingModeling and SimulationModelling and SimulationMatrix splitting methodsRegular and weak regular splittingsDomain decompositionAlgebraic numberQualitative analysisMathematics

description

Abstract Qualitative properties of matrix splitting methods for linear systems with tridiagonal and block tridiagonal Stieltjes-Toeplitz matrices are studied. Two particular splittings, the so-called symmetric tridiagonal splittings and the bidiagonal splittings, are considered, and conditions for qualitative properties like nonnegativity and shape preservation are shown for them. Special attention is paid to their close relation to the well-known splitting techniques like regular and weak regular splitting methods. Extensions to block tridiagonal matrices are given, and their relation to algebraic representations of domain decomposition methods is discussed. The paper is concluded with illustrative numerical experiments.

10.1016/s0898-1221(01)00221-8http://dx.doi.org/10.1016/s0898-1221(01)00221-8