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
- SzegÃ¶'s theorem

An uncategorized list of references of high pedagogic value.

An Introduction to the Conjugate Gradient Method Without the Agonizing Pain by Jonathan Richard Shewchuk (1994)

Toeplitz and Circulant Matrices: A Review by Robert M. Gray (2006)

Scalable Inference for Structured Gaussian Process Models, Chapter 5

^{a}by Yunus SaatÃ§i (2011)The Matrix Cookbook by Kaare Brandt Petersen, Michael Syskind Pedersen (2012)

Discovering Transforms: A Tutorial on Circulant Matrices, Circular Convolution, and the Discrete Fourier Transform by Bassam Bamieh (2018)

- Numerical Linear Algebra by Lloyd N. Trefethen and David Bau, III (1997)

- Includes description, properties and an application of Kronecker-factored matrices.â†©