Chapter 1: #18-19,21-28
Chapter 2: #8
Due: Oct 18 (Tue) or 19 (Wed) in your tutorial.
Friday, September 30, 2016
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
Interpolation in two dimensions.
Scattered data: triangulation and then piecewise linear interpolation.
Structured data: bilinear interpolation
Wednesday, September 28, 2016
Friday, September 23, 2016
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.
Interpolation: Polynomial interpolation.
Lagrange Interpolating Polynomial. We will prove the error estimate in the next lecture.
Wednesday, September 21, 2016
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 $m$.
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 $m$.
Tuesday, September 20, 2016
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.
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.
Tuesday, September 13, 2016
Lecture 4 (Sep 14)
Error estimates for fixed point iterations.
Newton's method. Geometrical construction. Convergence.
Secant method.
Newton's method. Geometrical construction. Convergence.
Secant method.
Friday, September 9, 2016
HW1
HW set: [click here]
Chapter 1: #1-8
Chapter 2: #1,3,4
Due: Sep 20 (Tue) or 21 (Wed) in your tutorial.
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.
Fixed Point Iteration: Method.
Fixed Point Theorem (Thm 2.3 from the textbook).
Example.
Error estimates.
Thursday, September 8, 2016
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.
1) Bisection method. Algorithm. Convergence and an error estimate.
2) Fixed point iteration. Definition of fixed point. Existence and Uniqueness of a fixed point.
Thursday, September 1, 2016
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
Numerical/Computer Arithmetic
IEEE 754 standard
Integers (4 bytes), single precision (4 bytes), double precision (8 bytes)
Machine epsilon
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