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日期:2020-05-06 10:33

Programming Project PART 2

CS 323 - Numerical Analysis

1 Introduction

For this second part of the project you will write matlab code for the following

algorithms. Instructions are the same as in the first part of the project.

2 Algorithms

The following is the list of all the algorithms that you must implement for this

second part:

1

1. Cubic Splines: Given a set of points find the coefficients of all the 3rd

degree polynomials that go through all the given points using the cubic

splines method.

Input:

Sample input representing the points (1, 5),(2, 6),(3, 6.5),(4, 5.5),(5, 5.5),(6, 7)

where the first number corresponds to the number of points.

Output:

(a) Coefficients of n?1 polynomials. The coefficients of each polynomial

in a row separated by spaces (see lecture notes for lecture 14):

5 1.014354 0 -0.014354

6 0.971291667 -0.043062 -0.42822967

6.5 -0.39952167 -1.327751 0.727272667

5.5 -0.87320567 0.854067 0.019138667

5.5 0.89234467 0.911483 -0.30382767

(b) A plot like the one shown on lecture notes (14).

2

2. Least Squares: Given a set of points you will find a polynomial of degree

n that approximates the points minimizing the error squared.

Input:

Sample input representing the points (0, 45.13),(1, 51.71),(2, 60.17),(3, 64.83),

(4, 65.24),(5, 65.17),(6, 67.65),(7, 79.8),(8, 96.13),(9, 115.19),

where the first number corresponds to the number of points and the second

number is the degree of the desired polynomial.

Output:

(a) The coefficients of the polynomial, separated by spaces:

43.9719 13.4363 -3.3048 0.3005

(b) A plot like the one shown on lecture notes (16).

3

3. Simpson’s Rule: Compute the definite integral of a given function using

the Composite Simpson’s rule.

Input: Function (of x) as a string (use matlab’s inline and feval), the

limits of integration (a and b), and the number of subintervals. Sample

input:

Output: The approximate value of

using Simpson’s rule with n subintervals

4


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