Gaussian elimination

(redirected from Gauss elimination)

Gaussian elimination

[¦gau̇·sē·ən ə‚lim·ə′nā·shən]
(mathematics)
A method of solving a system of n linear equations in n unknowns, in which there are first n- 1 steps, the m th step of which consists of subtracting a multiple of the m th equation from each of the following ones so as to eliminate one variable, resulting in a triangular set of equations which can be solved by back substitution, computing the n th variable from the n th equation, the (n- 1)st variable from the (n- 1)st equation, and so forth.
Mentioned in ?
References in periodicals archive ?
The computational cost of the previous procedure to compute accurately the LDU-factorization associated to Gauss elimination with symmetric m.
This phenomenon is similar to that of the backward error in Gauss elimination with partial pivoting, which is usually much smaller than the theoretical exponential bound.
16]) that diagonal dominance by rows or columns is inherited by the Schur complements obtained when performing Gauss elimination.
Although Gauss elimination without pivoting of a positive definite symmetric matrix is stable, it does not guarantee the well conditioning of the triangular factors.
pivoting interchanges the first and second rows and columns in the first step of Gauss elimination and it still produces another row and column exchange in the second step.
3]) comparisons beyond the cost of Gauss elimination with no pivoting) and the rook pivoting (see [7], [15] and [9]), of lower computational cost (in the worst case, O([n.
2]) elementary operations beyond the cost of Gauss elimination with no pivoting.
But it has few modifications over the Gauss elimination method.
The implementation of the Gauss Elimination algorithm on several parallel machines using shared memory design and message passing programming model is reported in [2].
The number of arithmetic operations is more in Gauss Jordan method (150) than in Gauss Elimination method (136) since Gauss Jordan method uses backward elimination step.
But the total number of instructions is more for Gauss elimination method.
Brooks III, Gauss Elimination : A case study on Parallel Machines, IEEE International Conference, Compcon Spring '91, March 1991.