Task 4: Stability of Gaussian Elimination Higham (9.13 and 9.14) gives a historical perspective and notes on LU factorization. Use this as a starting point for a literature search. (a)Views on Gaussian Elimination with Partial Pivoting (GEPP) have changed over time. Give a half page summary of the history of the understanding of GEPP, listing the some of the key papers which have changed our understanding. Try to include at least one paper not mentioned in Higham 9.13 or 9.14. The rounding error analysis in GE was pioneered and became a method for the determination of extent errors and arising from the analysis. Commonly, a short forward error analysis technique was thereafter coined. It was assumed that /aij/<1 and /b/<1 and a factor of 4n-1 for the error in the elements of the reduced upper triangular system. Nueman and Goldstine (1200, 1947) subsequently provided a long and difficult rigorous fixed-point analysis for the inversion of a symmetric positive definite matrix A via GE. He showed that the computed inverse X satisfies //Ax-I//z<14.2n2
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