Math 128B

Numerical analysis

MWF 15:10-16:00, 85 Evans Hall

Topics covered so far

• 01/19: Introduction to MATLAB.
• 01/21: Vector norms.
• 01/24: Matrix norms.
• 01/26: Eigenvalues, eigenvectors, and normal forms.
• 01/28: The power method.
• 01/31: Jacobi and Gauss-Seidel methods.
• 02/02: Relaxation methods.
• 02/04: Error bounds and iterative refinement.
• 02/07: Conjugate gradient method.
• 02/09: More on the conjugate gradient method.
• 02/11: Preconditioned conjugate gradient method.
• 02/14: Householder transformations.
• 02/16: QR algorithm.
• 02/21: Introduction to numerical ODEs; Euler's method.
• 02/23: Midterm #1 on matrix algorithms.
• 02/25: Review of the midterm and homework on matrix algorithms.
• 02/28: Heun's method; Taylor's methods for I.V.P.
• 03/02: Runge-Kutta methods for I.V.P.
• 03/04: Linear shooting for B.V.P.
• 03/07: Finite-difference method for linear B.V.P.
• 03/09: Nonlinear shooting for B.V.P.
• 03/11: Finite-difference method for nonlinear B.V.P.
• 03/14: Introduction to B.V.P. for PDEs
• 03/16: Hyperbolic PDEs
• 03/18: Parabolic PDEs
• 03/28: Elliptic PDEs
• 03/30: Introduction to splines. Cardinal B-splines.
• 04/01: B-splines on non-uniform knot sequences: definition, basic properties
• 04/04: Midterm #2 on numerical ODEs and PDEs.
• 04/06: Discussion of the midterm.
• 04/08: Marsden's identity and consequences.
• 04/11: De Boor-Fix linear functionals.
• 04/13: Evaluation, differentiation, knot multiplicity.
• 04/15: Stability of the B-spline basis. Control polygon.
• 04/18: Knot insertion.
• 04/20: Variation diminution. The ppform.
• 04/22: The ppform, continued. Polynomial interpolation (review).
• 04/25: Spline interpolation.
• 04/27: Bernstein polynomials and Bezier curves.
• 04/29: Bezier curves II.
• 05/02: Subdivision I.
• 05/04: Subdivision II.
• 05/06: J.Dorfman's lecture: subdivision on Bezier curves.
• 05/09: Review: Q. and A. session.

Resources

• Books.
• Numerical methods using MATLAB, by John H. Mathews and Kurtis D. Fink, 4th edition.
• Numerical analysis, by Richard L. Burden and J. Douglas Faires, 7th edition.
• Numerical analysis in modern scientific computing, by Peter Deuflhard and Andreas Hohmann, 2nd edition.
• Accuracy and stability of numerical algorithms, by Nicholas J. Higham. 2nd edition.

Lectures will be based primarily on the first two books and on spline notes by Carl de Boor.

• Jonathan Dorfman's website for Math 128B.
• Carl de Boor's lecture notes on splines, also available in in PDF.

The instructor welcomes cooperation among students and the use of books. However, handing in homework that makes use of other people's work (be it from a fellow student, a book or paper, or whatever) without explicit acknowledgement is considered academic misconduct.

Assignments

• Homework assignment #1, due Jan 26th, in PS and in PDF.
• Homework assignment #2, due Feb 2nd, in PS and in PDF.
• Homework assignment #3, due Feb 9th, in PS and in PDF.
• Homework assignment #4, due Feb 16th, in PS and in PDF.
• Homework assignment #5, due Feb 23rd, in PS and in PDF.
• Homework assignment #6, due Mar 7th, in PS and in PDF.
• Homework assignment #7, due Mar 16th, in PS and in PDF.
• Homework assignment #8, due Mar 28th, in PS and in PDF.
• Homework assignment #9, due Apr 15th, in PS and in PDF.
• Homework assignment #10, due Apr 27th, in PS and in PDF.
• Homework assignment #11, due May 6th, in PS and in PDF.

Solutions

All solutions were prepared by Jonathan Dorfman.

Misc. handouts

• Mock midterm #1, in PS and in PDF.
• Actual midterm #1, in PS and in PDF.
• Mock midterm #2, in PS and in PDF.
• Mock final, in PS and in PDF.

Demos, m-files, etc.

The first MATLAB diary and the corresponding plots graph1.eps and fig1.ps.