Math 4353/5393 – Numerical Linear Algebra Fall 2020 Program 4 Due Wednesday, April 15, 2020 1. Write the subroutine houseqr to compute the QR factorization. houseqr.m should have as its first line:...

I have attached my programming assignment in the attachment. The program should be in matlab


Math 4353/5393 – Numerical Linear Algebra Fall 2020 Program 4 Due Wednesday, April 15, 2020 1. Write the subroutine houseqr to compute the QR factorization. houseqr.m should have as its first line: function [A,u1] = houseqr(A) It should implement the Householder QR factorization without explicitly forming Q. The ũk vectors should overwrite A in the strictly lower triangle, and the uk(1) scalars should be stored in u1(k). R will be stored in the upper triangle of A. 2. Write the subroutine houseqtact to compute Qtb, given the “decapitated” u1, . . . , un stored in the strictly lower triangle of Qu and their “heads” in u1. houseqact.m should have as its first line: function y = houseqtact(Qu,u1,b) It should implement the algorithm we discussed in class/handout to find Qtb. 3. Also send me the output, prog4run, of the test routine NLAProg4test.m Notes: (a) For efficiency, we do not form Q explicitly when doing the Householder QR factorization, we just save the ũi over the columns of A. This is why we need the HOUSEQTACT routine. (b) Please notice how this admittedly opaque storage scheme results in remarkably little data movement and efficient memory use. (c) Remember to document your code. This means using comment lines to describe all input and output variables, and to describe what the code is doing when it is not obvious to the uninitiated. (d) You might be interested to see how this method compares to your mgs and cgs code. If you have the interest, try running a test to see which, if either, of xqr or xmgs or xcgs is consistently closer to xtrue.