# MATH 849 (07764), Spring 2010

## Topics in Applied Mathematics

Catalog Description:
Selected topics not covered in regular offerings.
Description:
We will continue the topics started in MATH 629 Numerical Analysis: Linear Algebra.
Desired Learning Outcomes:
Students will have a deep understanding of numerical methods for linear algebra. They will know the standard methods and be able to analyze and learn new methods on their own.
Prerequisites:
MATH 629.
Instructor:
Martin J. Mohlenkamp, mohlenka@ohio.edu, (740)593-1259, 315B Morton Hall.
Office hours: Monday 9:10-10am, Tuesday 9:10-10am, Thursday 9:10-10am, and Friday 9:10-10am.
Web page:
http://www.ohio.edu/people/mohlenka/20103/849.
Class hours/ location:
MTuThF 1:10-2pm in 315B Morton Hall.
Text:
Numerical Linear Algebra, by Lloyd N. Trefethen and David Bau III. Society for Industrial and Applied Mathematics, 1997; ISBN 978-0-898713-61-9. We will cover sections 25-40
Format:
The students will divide the topics in each section amongst themselves and present the topics to each other. They will select two homework problems from each section, collectively produce solutions, and present them in class.
The course will be graded CR or F. Students who attend and present as described above will receive CR.
Section Homework
Part V: Eigenvalues
25: Overview of Eigenvalue Algorithms 25.1 and 25.3
26: Reduction to Hessenberg or Tridiagonal Form 26.1
27: Rayleigh Quotient, Inverse Iteration 27.1 and 27.4
28: QR Algorithm without Shifts 28.2 and 28.3
29: QR Algorithm with Shifts 29.1
30: Other Eigenvalue Algorithms 30.1 and 30.3
31: Computing the SVD 31.3 and 31.4
Part VI: Iterative methods
32: Overview of iterative Methods 32.1 and 32.2
33: The Arnoldi Iteration 33.1 and 33.2
34: How Arnoldi Locates Eigenvalues 34.1 and 34.2
35: GMRES 35.1 and 35.2
36: The Lanczos Iteration 36.1 and 36.3
37: From Lanczos to Gauss Quadrature 37.1 and 37.4
38: Conjugate Gradients 38.5 and 38.6
39: Biorthogonolization Methods 39.1 and 39.5
40: Preconditioning 40.1 and 40.2

Martin J. Mohlenkamp