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Quantum Gauß Jordan Elimination
, 2005
"... In this paper we construct Gauß Jordan Elimination (QGJE) Algorithm and estimate the complexity time of computation of Reduced Row Echelon Form (RREF) of an N×N matrix using QGJE procedure. The main theorem asserts that QGJE has computation time of order 2 N/2. 1 ..."
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In this paper we construct Gauß Jordan Elimination (QGJE) Algorithm and estimate the complexity time of computation of Reduced Row Echelon Form (RREF) of an N×N matrix using QGJE procedure. The main theorem asserts that QGJE has computation time of order 2 N/2. 1
On the Stability of GaussJordan Elimination with Pivoting
"... The stability of the GaussJordan algorithm with partial pivoting for the solution of general systems of linear equations is commonly regarded as suspect. It is shown that in many respects suspicions are unfounded, and in general the absolute error in the solution is strictly comparable with that co ..."
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with that corresponding to Gaussian elimination with partial pivoting plus back substitution. However, when A is ill conditioned, the residual corresponding to the GaussJordan solution will often be much greater than that corresponding to the Gaussian elimination solution.
GaussJordan Elimination Method in Verilog
"... It gives the architecture of an optimized complex matrix inversion using GAUSSJORDAN (GJ) elimination in Verilog with single precision floatingpoint representation. The GJelimination algorithm uses a single precision floating point arithmetic components and control unit for performing necessary a ..."
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It gives the architecture of an optimized complex matrix inversion using GAUSSJORDAN (GJ) elimination in Verilog with single precision floatingpoint representation. The GJelimination algorithm uses a single precision floating point arithmetic components and control unit for performing necessary
Parallel GaussJordan elimination for the solution of dense linear systems *
, 1987
"... Abstract. Any factorization/back substitution scheme for the solution of linear systems consists of two phases which are different in nature, and hence may be inefficient for parallel implementation on a single computational network. The GaussJordan elimination scheme unifies the nature of the two ..."
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Abstract. Any factorization/back substitution scheme for the solution of linear systems consists of two phases which are different in nature, and hence may be inefficient for parallel implementation on a single computational network. The GaussJordan elimination scheme unifies the nature
An Explicit Construction of GaussJordan Elimination Matrix ✩
, 907
"... A constructive approach to get the reduced row echelon form of a given matrix A is presented. It has been shown that after the kth step of the GaussJordan procedure, each entry a k ij(i = j, j> k) in the new matrix A k can always be expressed as a ratio of two determinants whose entries are fro ..."
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A constructive approach to get the reduced row echelon form of a given matrix A is presented. It has been shown that after the kth step of the GaussJordan procedure, each entry a k ij(i = j, j> k) in the new matrix A k can always be expressed as a ratio of two determinants whose entries
Efficient Matrix Inversion Via GaussJordan Elimination and . . .
, 1998
"... We present a new parallel matrix inversion algorithm and report its implementation on parallel computers with distributed memory. The algorithm features natural load balance, simple programming and easy performance optimization, while maintaining the same arithmetic cost and numerical properties of ..."
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We present a new parallel matrix inversion algorithm and report its implementation on parallel computers with distributed memory. The algorithm features natural load balance, simple programming and easy performance optimization, while maintaining the same arithmetic cost and numerical properties of the conventional inversion algorithm. Our analysis and experiments on a cray t3e report nearpeak performance for the new approach.
A note on the stability of GaussJordan elimination for diagonally dominant matrices
"... Peters and Wilkinson [4] state that "it is well known that GaussJordan is stable" for a diagonally dominant matrix, but a proof does not seem to have been published [3]. The present note fills this gap. GaussJordan elimination is backward stable for matrices diagonally dominant by rows a ..."
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Peters and Wilkinson [4] state that "it is well known that GaussJordan is stable" for a diagonally dominant matrix, but a proof does not seem to have been published [3]. The present note fills this gap. GaussJordan elimination is backward stable for matrices diagonally dominant by rows
An Alternative Method to GaussJordan Elimination: Minimizing Fraction Arithmetic
"... When solving systems of equations by using matrices, many teachers present a GaussJordan elimination approach to row reducing matrices that can involve painfully tedious operations with fractions (which I will call the traditional method). In this essay, I present an alternative method to row reduc ..."
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When solving systems of equations by using matrices, many teachers present a GaussJordan elimination approach to row reducing matrices that can involve painfully tedious operations with fractions (which I will call the traditional method). In this essay, I present an alternative method to row
Note on the stability of GaussJordan elimination for diagonally dominant matrices
, 1999
"... Peters and Wilkinson [4] state that "it is well known that GaussJordan is stable" for a diagonally dominant matrix, but a proof does not seem to have been published [3]. The present note fills this gap. GaussJordan elimination is backward stable for matrices diagonally dominant by rows a ..."
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Cited by 4 (0 self)
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Peters and Wilkinson [4] state that "it is well known that GaussJordan is stable" for a diagonally dominant matrix, but a proof does not seem to have been published [3]. The present note fills this gap. GaussJordan elimination is backward stable for matrices diagonally dominant by rows
Results 1  10
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1,924