MTP290 Assignment 2 Solved

Description

 

1. (a) Then solve the linear system Ax = b using the above matrices L and U.

The code should work for any non-singular square matrix A. Use a proper A and b to verify the results.

2.  Find the conditional number of the following matrix for n = 3,4,3,5,6 using the row-norm, column-norm and Euclidean-norm. Do not use the inbuilt norm function from the Matlab library. What do you observe in the results?

 .

3.  A tridiagonal system with n unknowns is given by,

a_ix_i−1 + b_ix_i + c_ix_i+1 = d_i; i = 1,2,…,n

where a₁ = c_n = 0. Solve the above system using the following method which is a special case of Gaussian elimination method:

;                    ;    i = 1

;;                                            i = 2,3,…,n.

xn = d0n x_i = d⁰_i − c⁰_ix_i+1 ; i = n − 1,n − 2,…,1.

Instructions:

• Any descriptive answer should be written at the top of the code. Use ‘%’ to comment inside the code.
• Make Matlab script for each of the above problems and submit only the ‘.m’ file in gradescope.
• The final code should run without any error. Sample inputs required for the code should be specified by yourself.
• Code will be checked manually. Checker will only hit run, and he/she will not provide any input during checking. Everything should be specified in each code. Please do not take the risk of copying or sharing your code with classmates.

Code similarity will be checked.

• For any clarification feel free to comments on team under this assignment posted.
• No partial marks will be given unless you use the correct method for each question. For example, use of general Gaussian elimination method in question 3 will be entitled a zero mark.

1