# 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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Usually, the Gaussian elimination method requires a storage of O([K.sup.2]) and a computational cost of O([K.sup.3]).
In the paper "Gaussian Elimination-Based Novel Canonical Correlation Analysis method for EEG Motion Artifact Removal," they improved the canonical correlation analysis (CCA)  based approach by introducing Gaussian elimination method, called GECCA.
3) Simply using the Gaussian Elimination for decoding is not conducive to the restoration of source data.
We notice that as the matrices are sparse and structured, we can also use Gaussian elimination for solving the shifted linear systems.
Less obvious, so contestable, examples might include Gaussian elimination and numerical integration.
Standard direct methods based on the Gaussian elimination require more work than iterative schemes.
Thus, (11) constitutes n-equations in n-unknowns which can be determined by using Gaussian elimination method.
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  and Gaussian elimination .
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.
SISO decoding of RS code consists of three stages, which includes Gaussian elimination, belief propagation or sum-product algorithm, and RS hard decision decoding.
Gaussian elimination technique will be used for execution time comparison.

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