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Lectures

About the lecture series

The History of Numerical Analysis at Stanford lecture series was a joint effort, organized in 2007, between the SIAM Student Chapter at Stanford and the Linear Algebra and Optimization seminar at the iCME to

i) educate current students about who did what and when they did it at Stanford and increase awareness of the contributions of Stanford affiliates in the field,

ii) promote more student involvement and interest by removing some of the mystique of numerical analysis and computational mathematics through historical presentations, and

iii) raise awareness of computational mathematics for the "50 Years of Computational Mathematics at Stanford" conference at the end of March 2007.

Appearing below are the original abstracts for the talks that were given as part of the series, as well as links to the videos of the talks.

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Golub (February 8th, 2007)

Professor Gene Golub of the Computer Science department spoke about his personal voyage in developing numerical algorithms. In his own words:

For over 40 years, I have been actively involved in developing numerical algorithms. The methods developed came about through the need of solving problems which often came from applications. Interestingly enough, each method often led to the need of others. In this talk, I will describe how these algorithms were developed sequentially.

Here are some algorithms/methods I shall describe.

* Cyclic Reduction
* Fast Poisson Solvers
* Domain Decomposition
* Generalized CG
* Bidiagonalization of Matrices
* Singular Value Decomposition

Slides

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Pereyra (February 21st, 2007)

Dr. Victor Pereyra of Weidlinger Associates Inc. spoke about his experiences with numerical analysis at Stanford:

I have been involved with the Numerical Analysis group at Stanford since 1963, first as a student and later on as a frequent visitor, invited Faculty, Lecturer, and friend. In this lecture I will describe some of the research produced at Stanford during these years, from pseudoinverses, through deferred corrections, error estimators, equidistributed meshes, fast Vandermonde solvers with generalizations to multiple dimensions, and seismic ray tracing (whatever fits in 45 minutes!).

Slides

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Gustafsson (February 28th, 2007)

Professor Bertil Gustafsson of Upssala University spoke about his experiences with numerical analysis and partial differential equations at Stanford along with discussing Joseph Oliger's work:

Numerical methods for partial differential equations have been an active area of research at Stanford for many years. As a frequent visitor here, I have had the opportunity to collaborate with faculty, visitors and students over the years. Joe Oliger represented the PDE area at the Computer Science Department for 27 years, and I will give a brief survey of what he and his students were working on, as well as some background leading up to his employment here. I will also make some comments about the work by well known PDE people at other departments at Stanford.

Slides

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Ye (March 7th, 2007)

Professor Yinyu Ye of the Management Science and Engineering department spoke about Linear Programming at Stanford with an emphasis on George Dantzig's work and some applications:

Linear programming (LP) is becoming a more and more important and popular mathematical and numerical optimization model/tool in everyday and every field's decision making. Businesses, large and small, now use LP to control manufacture inventories, price commodities, design civil/communication networks, and plan investments. LP has also become a popular subject taught in under/graduate and MBA curricula, advancing human knowledge and promoting science education. We will present a few historical results of George Dantzig on LP and their impact on the field of computational mathematics and engineering. We will also present a few modern applications arisen from exchange market pricing and call auction mechanism designing. LP today is proven to be an extremely effective theory-proving machine as well. We will show a couple of such examples in coding theory and approximation algorithms for discrete optimization, together with some remaining open questions in LP.

Slides (if your Web browser cannot open this large file, which is approximately 7 MB, then you can try to download it and then view it using another software application)

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Saunders (March 14, 2007)

Professor Michael Saunders of the Management Science and Engineering department spoke about the history of stable numerical optimization at Stanford. In his own words:

I came to Stanford in 1967 as a very green graduate student (not in today's ecological sense). Computer Science was a new department, as was Operations Research. The CS qualifying exams allowed 3 out of 5 topics, including numerical analysis. Alan George and I obtained permission to take one of the OR exams. Thus began a career of applying stable matrix methods to numerical optimization (as pioneered by Gene Golub, Philip Gill, and Walter Murray).

We trace the impact of Gene inviting numerous researchers to Serra House (including Chris Paige and Bruce Murtagh), as well as George Dantzig's creation of the Systems Optimization Lab in the OR Department, and Gene's founding of the SCCM Program.

Slides