[SOLVED] algorithm matlab Extra task NLAA Numerical Linear Algebra with Applications

Extra task NLAA Numerical Linear Algebra with Applications
Instructions: Please upload to Canvas by the end of the Friday lecture in week 8 (March 8) a single file corresponding to part (b) of the task below. Please name your file as suggested in the question.
Plagiarism check: Your electronic submissions should be your own work and should not be identical or similar to other submissions. A check for plagiarism will be performed on all submissions.
Let A Rnm have full rank and let b Rn. Consider the least squares problem: find the minimiser x Rm of the functional F : Rm [0,) given by
F(x) := b Ax2.
(a) Modify the algorithm for the LU-factorization with partial pivoting so that it constructs the
factorization
PA = LU, (1)
where P is a permutation matrix, U Rmm is upper triangular and L Rnm is unit lower triangular (i.e., for 1 i n, Lij = 0 if j > i and Lii = 1). Write a function file luppgen.m with A as input, while your output should be the factors LE,UE in the economy (thin) version of (1) and a permutation vector corresponding to P.
(b) Using the factorisation from part (a), derive the LU factorisation method for the least squares problem. Write a function file lslusolve.m to implement this method. Your input should be A,b, while your output should be the solution vector x. Your file should contain luppgen.m as a subfunction.
Note: You should submit the matlab file for this task only if you are registered on the LM version of this course (module code 27689), i.e., if you are a Year 4 or MSc student, or you registered specifically on the LM version as an exchange or Erasmus student.