The condition number of the Vandermonde matrix may be large, causing large errors when computing the coefficients if the system of equations is solved using Gaussian elimination.
42.
In this case, we can make use of the Sherman-Morrison formula to avoid the additional operations of Gaussian elimination and still use the Thomas algorithm.
43.
The fast elliptic solver is based on fast Fourier analysis in both horizontal directions and Gaussian elimination in the vertical direction ( Moussiopoulos and Flassak, 1989 ).
44.
:: Yeah, according to the article Gaussian elimination can be performed over any field . talk ) 08 : 16, 15 February 2008 ( UTC)
45.
Some authors use the term Gaussian elimination to refer to the process until it has reached its upper triangular, or ( non-reduced ) row echelon form.
46.
The notes were widely imitated, which made ( what is now called ) Gaussian elimination a standard lesson in algebra textbooks by the end of the 18th century.
47.
The development of computers led to increased research in efficient algorithms for Gaussian elimination and matrix decompositions, and linear algebra became an essential tool for modelling and simulations.
48.
Even for a well conditioned full rank matrix, Gaussian elimination does not behave correctly : it introduces rounding errors that are too large for getting a significant result.
49.
Unfortunately, applying Gaussian elimination ( or equivalently an LU decomposition ) to such a matrix results in the band being filled in by many non-zero elements.
50.
Solving such a linear system is not practical due to extremely high time complexity of solving a linear system by the means of Gaussian Elimination or even Strassen algorithm.
