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instead of fortran, use MATLAB Exercise 3.3.9 Write a pair of Fortran subroutines to solve the least squares problem for the overdetermined system Ar b,
instead of fortran, use MATLAB
Exercise 3.3.9 Write a pair of Fortran subroutines to solve the least squares problem for the overdetermined system Ar b, where A ER*m, n > m, and A has full rank. 218 THE LEAST SQUARES PROBLEM The first subroutine uses reflectors to carry out a QR decomposition, A QR, where Q Rns product of reflectors: Q-QQm, and R Rnxm, where R is m-by-m and upper triangular. All of these operations should be carried out in a single n-by-m array plus one or two auxiliary vectors. If R has any zero pivots, the subroutine should set an error flag to indicate that A does not have full rank. The second subroutine uses the QR decomposition to find r. First cQTb QmQm-1. . Q1b is calculated by applying the reflectors successively. An additional one-dimensional array is needed for b. This array can also be used for c (and intermediate results). The solution x is found by solving Rx = by back substitution, . The solution should calculate ||d1, which is the Euclidean norm where cd of the residual. Use your subroutines to solve the following problemsStep by Step Solution
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