Numerical Algorithms Assignment 2 (Mini-Project)
数值算法作业代写 Plot curve r(u) using some software tools such as Matlab, the visualization tool provided in Appendix B, etc., which you prefer to use.
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:
Your discussion:
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
Your discussion:
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:
Your discussion:
T5.
The result:
Your discussion:
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