代写Linear Algebra、代做Canvas留学生、代做matlab编程语言、代写matlab代写-代写Matlab编程

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 ∈ R

n×m have full rank and let b ∈ Rn. Consider the least squares problem: find the minimiser

x ∈ R

m of the functional F : R

m → [0,∞) given by

F(x) := kb Axk2.

(a) Modify the algorithm for the LU-factorization with partial pivoting so that it constructs the

factorization

P A = LU, (1)

where P is a permutation matrix, U ∈ R

n×n

is upper triangular and L ∈ R

m×n

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.