Summer 2022: Classic Papers in Numerical Analysis

The reading group in the summer mimicked Trefethen's 13 Classic Papers in Applied Mathematics. Two presenters were assigned for each topic: one to focus on the mathematical details, and the other to code examples of the techniques being discussed. Below you can find a list of what topics we covered (in order). The linked articles were the main readings for the topic, however most presentations relied on several resources. If you're curious about other readings, feel free to reach out to Yichen Guo (ycguo at vt dot edu) or Sam Bender (s k bender at vt dot edu).

We appreciate Dr. Beattie and Dr. Embree for suggestions.

Fast Fourier Transform

• "An algorithm for the machine calculation of complex Fourier series" (Cooley & Tukey, 1965)

• Sam Bender (math) and Haroun Meghaichi (code)

Conjugate Gradient

• "Methods of conjugate gradients for solving linear systems" (Hestenes & Stiefel, 1952)

  • An Introduction to the Conjugate Gradient Method Without the Agonizing Pain

  • Some History of Conjugate Gradients and Other Krylov Subspace Methods

  • The conjugate gradient method from different perspectives

• Yichen Guo (code) and Ian Moore (math)

Multigrid

• "Multi-level adaptive solutions to boundary-value problems" (Brandt, 1977)

  • A Multigrid Tutorial

• Yichen Guo (math) and Haroun Meghaichi (code)

Overview of Finite Element Method & Finite Difference Method

• Haroun Meghaichi (math and code)

Stochastic Optimization

• "Adam: A Method for Stochastic Optimization" (Kingma & Ba, 2015)

• Sam Bender (math, notes) & Dan Folescu (code)

Multipole

• "A fast algorithm for particle simulations" (Greengard & Rokhlin, 1981)

  • A pedestrian introduction to fast multipole methods

  • Introduction to Fast Multigrid Methods

• Dan Folescu (code) and Yichen Guo (math)