HW3

Chapter 1: #18-19,21-28
Chapter 2: #8

Due: Oct 18 (Tue) or 19 (Wed) in your tutorial.

Lecture 8 (Sep 30)

Piecewise linear interpolation.

Interpolation in two dimensions.

Scattered data: triangulation and then piecewise linear interpolation.

A MATLAB implementation can be found here: [click here]

Structured data: bilinear interpolation

Lecture 7 (Sep 28)

Error estimate of using polynomial interpolation.

Newton's divided difference.

Lecture 6 (Sep 23)

Modified Newton's method for finding root with multiplicity m.

Interpolation: Polynomial interpolation.

Lagrange Interpolating Polynomial. We will prove the error estimate in the next lecture.

Lecture 5 (Sep 21)

Order of convergence.

General fixed point iteration: For a converging iteration and if g'(p)!=0, the method converges only linearly.

Otherwise, if g'(p)=0 and g'' continuous and strictly bounded, we have at least quadratic convergence.

Modified Newton's method for finding root with multiplicity $m$.

HW2

Chapter 1: #10,12-17
Chapter 2: #5-7
Data file for #2.6: Schrodinger.mat

Due: Oct 4 (Tue) or 5 (Wed) in your tutorial.

Note: For Q1.16, the theorem is the one we discuss in Lecture 7 on Sep 28.

Note: For Q2.7, the statement in the bracket is not right. Please ignore it.

Lecture 4 (Sep 14)

Error estimates for fixed point iterations.

Newton's method. Geometrical construction. Convergence.

Secant method.

HW1

HW set: [click here]

Chapter 1: #1-8
Chapter 2: #1,3,4

Due: Sep 20 (Tue) or 21 (Wed) in your tutorial.

Lecture 3 (Sep 9)

Existence and Uniqueness of a fixed point. Example.

Fixed Point Iteration: Method.

Fixed Point Theorem (Thm 2.3 from the textbook).

Example.

Error estimates.

Lecture 2 (Sep 7)

Root-finding
1) Bisection method. Algorithm. Convergence and an error estimate.
2) Fixed point iteration. Definition of fixed point. Existence and Uniqueness of a fixed point.

Lecture 1 (Sep 1)

Course overview

Numerical/Computer Arithmetic
IEEE 754 standard
Integers (4 bytes), single precision (4 bytes), double precision (8 bytes)
Machine epsilon

HW, Past Papers

[Click here]