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» Computing Rational Forms of Integer Matrices
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JSC
2002
58views more  JSC 2002»
13 years 5 months ago
Computing Rational Forms of Integer Matrices
Mark Giesbrecht, Arne Storjohann
FOCS
2000
IEEE
13 years 10 months ago
Computing the Determinant and Smith Form of an Integer Matrix
A probabilistic algorithm is presented to find the determinant of a nonsingular, integer matrix. For a matrix A ¡£¢ n¤ n the algorithm requires O¥ n3¦5 ¥ logn§ 4¦5§ bit...
Wayne Eberly, Mark Giesbrecht, Gilles Villard
FSTTCS
2006
Springer
13 years 10 months ago
Unbiased Rounding of Rational Matrices
Rounding a real-valued matrix to an integer one such that the rounding errors in all rows and columns are less than one is a classical problem. It has been applied to hypergraph co...
Benjamin Doerr, Christian Klein
DAGSTUHL
2008
13 years 7 months ago
Error Bounds for Lanczos Approximations of Rational Functions of Matrices
Abstract. Having good estimates or even bounds for the error in computing approximations to expressions of the form f(A)v is very important in practical applications. In this paper...
Andreas Frommer, Valeria Simoncini
VLSID
2002
IEEE
91views VLSI» more  VLSID 2002»
14 years 6 months ago
Rational ABCD Modeling of High-Speed Interconnects
This paper introduces a new numerical approximation technique, called the Differential Quadrature Method (DQM), in order to derive the rational ABCD matrix representing the high-s...
Qinwei Xu, Pinaki Mazumder