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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Less obvious, so contestable, examples might include Gaussian elimination and numerical integration.
Then one could use the same argument that Feinstein uses to "prove" that it is impossible to determine in polynomial-time whether this modified SUBSET-SUM equation has a solution, when in fact one can use Gaussian elimination to determine this information in polynomial-time.
The first extensive test bed is two real-world problem DAGs, molecular dynamics code [38] and Gaussian elimination [8].
Disimplicial arcs are important when Gaussian elimination is performed on a sparse matrix, as they correspond to the entries that preserve zeros when chosen as pivots.
Gaussian elimination then reduces the first independent m(n - k) columns to identity submatrix.
Gaussian elimination technique will be used for execution time comparison.
Gaussian elimination and its applications are covered next, followed by eigenvalues, eigenvectors, and determinants.
He laughed, he has experienced the same problem and our discussion went to direct methods, to Gaussian elimination and to Gram-Schmidt orthogonalization algorithms.
Systems of linear equations can be reduced to simpler form [21] by using Gaussian elimination method.
Hart does offer much to think about, however--among other things, that Gaussian elimination and general solutions of systems of linear equations are ultimately of non-literate origin and attested in China some seventeen centuries before Gauss.
includes chapters on Gaussian elimination and its variants, sensitivity of linear systems, the least squares problem, the singular value decomposition, eigenvalues and eigenvectors, and iterative methods for linear systems.
The Gaussian elimination method comprises of two steps, namely the forward elimination phase and the backward substitution phase.

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