﻿ 数值算法作业代写 Numerical Algorithms代写 - 作业代写, 算法代写

# 数值算法作业代写 Numerical Algorithms代写

2022-05-18 11:59 星期三 所属： 作业代写 浏览：95 ## Numerical Algorithms Assignment 2 (Mini-Project)

This assignment gives you a chance to practise numerical techniques (such as least-squares approximation, cubic B-spline interpolation, trigonometric interpolation, and numerical integration) on a parametric curve.

### Each of you is given an individual planar curve represented parametrically by  数值算法作业代写

r(u) = (x(u), y(u)) where and h is your index number in the class attendance list given in Appendix A. You are required to do the following tasks:

T1. (10 marks) Plot curve r(u) using some software tools such as Matlab, the visualization tool provided in Appendix B, etc., which you prefer to use.

T2. (25 marks) Propose a least-squares method to fit a parametric cubic polynomial curve to curve r(u) (hints: sample a few points on the curve and fit a cubic polynomial curve to the points). Plot your cubic polynomial curve and discuss how to choose the sampling points.  数值算法作业代写

T3. (25 marks) Using the cubic B-spline interpolation algorithm you implemented in Assignment 1, propose a method to approximate curve r(u) by a cubic B- spline curve (hints: sample at least 10 points on the curve and find a cubic B- spline curve interpolating these points). Plot your cubic B-spline curve and discuss what will affect the approximation result.

#### T4.

(25 marks) Using discrete Fourier Transform, propose a method to approximate curve r(u) by a trigonometric interpolation curve that can be represented by the following basis functions: Plot your trigonometric interpolation curve and discuss the result.

T5. (15 marks) Using composite Simpson’s rule, compute and discuss your result.

### Appendix B. Visualization tool  数值算法作业代写

This software tool has two versions: one for PC and the other for Mac. It allows the user to enter function definitions, domains of the input variables, and sampling resolution.

Example: to display the parametric curve

we enter the functions x(u) and y(u), the domain [0,1] and the resolution 100 into the program as follows: Syntax: Mathematical operations and functions that can be used in formulas are:

(, ), +, – , *, /, ^, sin, cos, tan, exp, sqrt, fabs, asin, acos, atan, atan2, cosh, fmod, log, log10, sinh, tanh, ceil, floor, min, max

For example, x^3 stands for x*x*x.

### Appendix C. Report format数值算法作业代写

Assignment 2 Report

Your name: XXX Matric No.: YYY

T1.

The plot of the curve:

T2.

Description or setup of your least-squares method:

The expression (i.e., representation) of your final cubic polynomial curve: The plot of your cubic polynomial curve:

T3.

Description or setup of your cubic B-spline interpolation method:

The expression (i.e., the representation) of your final cubic B-spline curve: The plot of your cubic B-spline curve:   数值算法作业代写

T4.

Description or setup of your method:

The expression (i.e., representation) of your final trigonometric interpolation curve:

The plot of your trigonometric interpolation curve:

T5.

The result: 