Problem 5: Forward and Backward Error Find the forward and backward error for the following functions, where the root is 3/4 and the approximate root is xa = 0.74: (a) f(x) (a) f(a) = 4x - 3 (A 213 (b) f(x) (d) floa) = (4x - 3)² Un 2)1/3

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LUP Decomposition

LU decomposition stands for Lower-Upper decomposition. LU decomposition is the factorization of the lower triangular matrix and an upper triangular matrix. It is very useful in linear algebra and numerical analysis. A permutation matrix is usually included in the product. Gaussian elimination in a matrix form is known as LU decomposition, When inverting a matrix or evaluating its determinant, this is a crucial step. Tadeusz Banachiewicz, a Polish mathematician, first proposed the LU decomposition in 1938.