CAAM 699 - Section 2
Math Sciences VIGRE Seminar
Topics in Dimension Reduction
Fall 2007

About this Course

Model reduction (a form of dimension reduction) seeks to replace a large-scale system of differential or difference equations by a system of substantially lower dimension that has nearly the same response characteristics. There are extensive applications in circuit simulation, fluid dynamics, structural dynamics, climate modeling and many others.

In the linear case, two main themes can be identified among methodologies.

Balanced (Gramian Based) Methods
Moment matching methods.

In the linear case, the development of these methods for large scale problems is currently a very active area of research. In the large scale setting, both approaches are best realized through Krylov subspace projection techniques similar to those used to iteratively solve large linear systems and eigenvalue problems. In the non-linear case, there is a wealth of literature including Proper Orthogonal Decomposition (POD) and Principal Component Analysis (PCA). However, these approaches are often ad-hoc and there is little known about the accuracy of these methods. This seminar will concentrate on understanding various nonlinear dimension reduction methods and on ways to extend some of the linear techniques such as balanced reduction to the nonlinear setting.

CAAM 699 (section 2) is a research seminar on dimension reduction. Seminar participation will consist of reading, discussing, and perhaps presenting current research and survey papers in various aspects of dimension reduction.

This seminar is suitable for graduate students at all levels, including first year students. CAAM undergraduates are also encouraged to participate.

Time and Room

Wednesdays 4-6pm in DH 1042.

The next class will be on Wednesday Sept. 19, 4pm in DH1042

Instructors

Matthias Heinkenschloss
Office: Duncan Hall 3088
Phone: x5176
Office Hours: by appointment
E-mail:heinken AT rice.edu

Danny C. Sorensen
Office: Duncan Hall 2035
Phone: x5193
Office Hours: by appointment
E-mail:sorensen AT rice.edu

Presentations

Note on Disability Based Accommodations

If you have a documented disability that will impact your work in this class, please contact me to discuss your needs. Additionally, you will need to register with the Disability Support Services Office in the Ley Student Center.