Topics in Numerical Analysis

The nicer and practical parts of linear algebra, differential equations, and optimization.
Aug 5, 2020Last updated: Dec 28, 2022

Numerical Linear Algebra

Numerical linear algebra is where rubber meets the road. This post collects some topics of interest to me. I aim to provide exposition better than standard textbooks whenever I can. Often times, ideas keep lying around deep inside 1000-page bibles.

  • Hutchinson Trace Estimator
  • Cholesky decomposition
    • Pivoted Cholesky decomposition
  • Preconditioning
  • Conjugate gradients
    • Modified Batched Conjugate Gradient Descent
  • Lanczos tridiagonalization
  • Kronecker-factored matrices
  • Toeplitz matrices
    • Szegö's theorem

References

An uncategorized list of references of high pedagogic value.

Lectures

Textbooks

Footnotes

  1. Includes description, properties and an application of Kronecker-factored matrices.

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