Undulant-block elimination and integer-preserving matrix inversion

Undulant-Block Elimination and Integer-Preserving Matrix Inversion

A new formulation for LU decomposition allows efficient representation of intermediate matrices while eliminating blocks of various sizes, i.e. during “undulantblock” elimination. Its efficiency arises from its design for block encapsulization, implicit in data structures that are convenient both for process scheduling and for memory management. Row/column permutations that can destroy such enc...

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Undulant - Block Elimination and Integer - Preserving Matrix Inversion 1 Technical Report 418

A new formulation for LU decomposition allows efficient representation of intermediate matrices while eliminating blocks of various sizes, i.e. during “undulantblock” elimination. Its efficiency arises from its design for block encapsulization, implicit in data structures that are convenient both for process scheduling and for memory management. Row/column permutations that can destroy such enc...

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Symmetric matrix inversion using modified Gaussian elimination

In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time’s spending. Further, both of them can be used efficiently not only for positive (semi-) definite, but for any non-singular symmetric matrix inversion. We use simulation to verify results, ...

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Fast symmetric matrix inversion using modified Gaussian elimination

In this paper we present two different variants of method for symmetric matrix inversion, based on modified Gaussian elimination. Both methods avoid computation of square roots and have a reduced machine time’s spending. Further, both of them can be used efficiently not only for positive (semi-) definite, but for any non-singular symmetric matrix inversion. We use simulation to verify results, ...

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Block tridiagonal matrix inversion and fast transmission calculations

A method for the inversion of block tridiagonal matrices encountered in electronic structure calculations is developed, with the goal of efficiently determining the matrices involved in the Fisher–Lee relation for the calculation of electron transmission coefficients. The new method leads to faster transmission calculations compared to traditional methods, as well as freedom in choosing alterna...

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Undulant-block elimination and integer-preserving matrix inversion

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