# Gaussian elimination

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## 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.
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In the first section they explain Gauss elimination, throwing in interesting tidbits to keep the interest of students who learned that in high school.
To solve this system of equation we used a factorization process that lead to the Gauss elimination method.
Authors like Turner [22] faced difficulty with Gauss Elimination approach because of round off errors and slow convergence for large systems of equations.
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.
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.
Our pivoting strategy needs to increase the computational cost of Gauss elimination in O([n.
FFT6, DCG4, and COLL refer to PELLPACK modules for sixth-order FFT nine-point differences, Dyakunov conjugate gradient with fourth-order accuracy, and collocation with band Gauss elimination, respectively.
PS5 is the five-point star module: a second-order finite-difference scheme with "as is" indexing and band Gauss elimination.
The authors have organized the main body of their text in seven chapters devoted to basic linear algebra subprograms, basic concepts for matrix computations, Gauss elimination and LU decompositions of matrices, and a wide variety of other related subjects.

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