Show that the LU Factorization Algorithm requires . 1 1 1 .3 - n multiplications/divisions and...

 

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Show that the LU Factorization Algorithm requires а. 1 1 1 .3 - n multiplications/divisions and 3" 1 1 - n + -n additions/subtractions. 2" b. Show that solving Ly b, where L is a lower-triangular matrix with l = 1 for all i, requires 1 2 1 n multiplications/divisions and 2" 2' n additions/subtractions. Show that solving Ax = b by first factoring A into A = Ux = y requires the same number of operations as the Gaussian Elimination Algorithm 6.1. Count the number of operations required to solve m linear systems Ax) by first factoring A and then using the method of part (c) m times. LU and then solving Ly = b and с. d. b) for k = 1, ..., m Show that the LU Factorization Algorithm requires а. 1 1 1 .3 - n multiplications/divisions and 3" 1 1 - n + -n additions/subtractions. 2" b. Show that solving Ly b, where L is a lower-triangular matrix with l = 1 for all i, requires 1 2 1 n multiplications/divisions and 2" 2' n additions/subtractions. Show that solving Ax = b by first factoring A into A = Ux = y requires the same number of operations as the Gaussian Elimination Algorithm 6.1. Count the number of operations required to solve m linear systems Ax) by first factoring A and then using the method of part (c) m times. LU and then solving Ly = b and с. d. b) for k = 1, ..., m