辅导Linear Algebra、讲解Canvas留学生、讲解matlab编程语言、辅导matlab
- 首页 >> OS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.
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.