Stability of Gaussian Elimination Higham

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Task 4: Stability of Gaussian EliminationHigham (9.13 and 9.14) gives a historical perspective and notes on LU factorization. Use this asa 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 someof the key papers which have changed our understanding. Try to include at least onepaper not mentioned in Higham 9.13 or 9.14.The rounding error analysis in GE was pioneered and became a method for thedetermination of extent errors and arising from the analysis. Commonly, a short forwarderror analysis technique was thereafter coined. It was assumed that /aij/<1 and /b/<1 anda factor of 4n-1for the error in the elements of the reduced upper triangular system.Nueman and Goldstine (1200, 1947) subsequently provided a long and difficult rigorousfixed-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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