本次加拿大代写是Matlab的一个assignment

Please read the following instructions carefully. If in doubt, please raise

issues in the discussion forum.

i) The submission deadline is 6pm on Tuesday of week 10.

ii) Please complete the template files provided through Moodle. Do not

change filenames or headers.

iii) Your code is not required to check whether a hypothetical user of your

code provides reasonable inputs.

iv) Symbolic computation and high-level Matlab commands are prohib-

ited and result in zero marks for the task in which they were used.

v) The marking scheme is full marks for a correct implementation and

no marks for an incorrect implementation.

vi) Submit a zip-file called firstname_surname_assignment_3.zip con-

taining all your Matlab files through Moodle.

**Assignment 3.1. (polynomial interpolation, 8 marks)**

In this exercise, you will see how polynomial interpolation behaves in com-

putational examples, and why we often use splines instead.

a) Complete the file myNewtonCoefficients.m by implementing an al-

gorithm that computes the scheme of divided differences. Recall that

the divided differences can be organised in a lower triangular matrix

as explained in Remark 5.7, and that the Newton coefficients can be

obtained as in Theorem 5.9.

b) Complete the file myEvaluateNewtonPolynomial.m by implementing

the Horner-type algorithm from remark 4.14.

c) Run the script wrapper_3_1.m, and relate the behaviour of the in-

terpolation polynomials generated by the wrapper to Theorem 5.13.

Compute the derivatives of the functions f used as test cases by the

wrapper to explain the output you see. (nothing to submit, not marked)

Assignment 3.2. (numerical differentiation, 2 marks)

In this exercise, you will see the interplay between the theoretical trunca-

tion error and the effect of round-o errors on the behaviour of numerical

dierentiation.

a) Complete the file myForwardDQ.m by implementing the forward differ-

ence quotient from Example 6.2.

b) Complete the file myCentralDQ.m by implementing the central differ-

ence quotient from Example 6.2.

c) Run the script wrapper_3_2.m, and explain as much of the output as

you can, based on statements from the lecture notes and exercises you

have completed. You cannot explain every detail, but most of what

you see in the plot. (nothing to submit, not marked)

**Assignment 3.3. (numerical integration, 6 marks)**

In this exercise, you will see in a computational example how composite

quadrature reduces the quadrature error when the integration interval is

divided into more and more subintervals.

a) Complete the file myTrapezoidal.m by implementing trapezoidal rule.

b) Complete the file mySimpson.m by implementing Simpson rule.

c) Complete the file myCompTrapezoidal.m by implementing the compos-

ite trapezoidal rule.

d) Complete the file myCompSimpson.m by implementing the composite

Simpson rule.

e) Run the script wrapper_3_3.m, and explain its output by referring to

the corresponding error estimates in the lecture notes. (nothing to

submit, not marked)