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Assignment 3 Answer

This document contains instructions for Assignment 3 in the course SIN 3005 Numerical Methods and Analysis. It lists 6 exercises involving finding least squares polynomial approximations and constructing orthogonal polynomials on different intervals for various functions. The assignment is due on November 18, 2021 and students must submit their solutions to the course team site.

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62 views35 pages

Assignment 3 Answer

This document contains instructions for Assignment 3 in the course SIN 3005 Numerical Methods and Analysis. It lists 6 exercises involving finding least squares polynomial approximations and constructing orthogonal polynomials on different intervals for various functions. The assignment is due on November 18, 2021 and students must submit their solutions to the course team site.

Uploaded by

dina
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd

Assignment 3

SIN 3005 Numerical Methods and Analysis


Institute of Mathematical Sciences
Universiti Malaya
(Orthogonal polynomials)

1. Find the linear least squares polynomial approximation to f ( x ) on the indicated


interval if
a) f ( x ) = x 2 + 3x + 2, [0,1];
b) f ( x ) = x3 , [0, 2];
1
c) f ( x ) = , 1,3 ;
x
d) f ( x ) = e x , [0, 2];
1 1
e) f ( x ) = cos x + sin 2 x, [0,1];
2 3
f) f ( x ) = x ln x, [1,3].

2. Find the least squares polynomial approximation of degree 2 to the functions and
intervals in Exercise 1.

3. Find the least squares polynomial approximation of degree 2 on the interval [−1, 1] for
the functions in Exercise 2.

4. Use the Gram-Schmidt process to construct 0 ( x ) , 1 ( x ) , 2 ( x ) , and 3 ( x ) for the


following intervals.
a)  0,1
b)  0, 2
c) 1,3

5. Repeat Exercise 1 using the results of Exercise 4.

1
Instructions:

1. All tutorial groups must answer all the questions.


2. Numerical softwares can be used to solve the questions.
3. The due date for Assignment 3 is 18/11/2021.
4. Please upload the solutions in Team SIN 3005.

2
ASSIGNMENT 3 SIN3005
GROUP 3

NUR NAJIA BINTI AHMAD ZAIDI 17133722/2


NURHANNANI BINTI BAHARUDIN 17104646/2
ILI SUHAILA BINTI MOHD NASAR 17120731/1
MUHAMMAD NAJMI BIN HAZLAN 17084513/2
FAREEZ ISKANDAR BIN ZAHARI 17127434/2
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