https://github.com/matsumotosan/numerical-linear-algebra

Jupyter notebooks on concepts from numerical/computational linear algebra. Inspired by Professor Rachel Thomas' class on computational linear algebra.
https://github.com/matsumotosan/numerical-linear-algebra

applied-linear-algebra computational-linear-algebra jupyter-notebook linear-algebra numerical-linear-algebra pytorch

Last synced: about 1 month ago
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Jupyter notebooks on concepts from numerical/computational linear algebra. Inspired by Professor Rachel Thomas' class on computational linear algebra.

• Host: GitHub
• URL: https://github.com/matsumotosan/numerical-linear-algebra
• Owner: matsumotosan
• Created: 2019-06-01T00:04:37.000Z (over 5 years ago)
• Default Branch: master
• Last Pushed: 2020-01-01T04:42:27.000Z (about 5 years ago)
• Last Synced: 2024-12-12T18:07:14.991Z (about 2 months ago)
• Topics: applied-linear-algebra, computational-linear-algebra, jupyter-notebook, linear-algebra, numerical-linear-algebra, pytorch
• Language: Jupyter Notebook
• Homepage:
• Size: 13.9 MB
• Stars: 1
• Watchers: 1
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Numerical Linear Algebra

[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/matsumotosan/numerical-linear-algebra/master)

Jupyter notebooks on concepts from numerical/computational linear algebra.

Inspired by [Professor Rachel Thomas' class on computational linear algebra](https://www.youtube.com/playlist?list=PLtmWHNX-gukIc92m1K0P6bIOnZb-mg0hY).

## Topics

### Introduction

- [x] p-norms

- [ ] Lp-spaces

- [x] Gauss-Legendre quadrature

### Matrix decomposition

- [x] SVD

  - [x] Truncated SVD

  - [x] Randomized SVD

- [x] Non-negative matrix factorization (NMF)

  - [x] Sparse NMF

- [x] Principal component analysis (PCA)

  -[x] Robust PCA

- [ ] QR factorization

  - [ ] QR algorithm with Wilkinson shifts

- [ ] Golub-Kahan bidiagonalization with Householder reflectors

### Eigenvalue algorithms

- [x] Power iteration

- [ ] Power method with shifts and deflation

- [x] Inverse iteration

- [ ] Rayleigh quotient iteration

- [ ] Arnoldi iteration

- [ ] Lanczos algorithm

- [ ] Cuppen's divide-and-conquer eigenvalue algorithm

### Clustering

- [ ] T-distributed stochastic neighbor embedding (t-SNE)

- [ ] *k*-means clustering

- [ ] *c*-means clustering

- [ ] Spectral clustering

### Preconditioners

- [x] Jacobi

- [x] Gauss-Seidel

- [x] Cholesky factorization

  - [x] Incomplete Cholesky with zero-fill (IC(0))

  - [ ] Incomplete Cholesky with threshold dropping (ICT)

- [x] LDL factorization

- [x] Successive over-relaxation (SOR)

- [ ] Symmetric successive over-relaxation (SSOR)

- [ ] Incomplete LU factorization (ILU)

- [ ] Sparse approximate inverse (SPAI)

- [ ] MR algorithm

### Iterative methods

- [x] Conjugate gradient (CG) method

  -[x] Preconditioned CG method

- [ ] Generalized minimal residual method (GMRES)

- [ ] Krylov subspaces

- [ ] Monte Carlo methods

## Other

- [ ] Sparseness measure

## Possible future topics

- Randomized linear algebra

## Creating Conda environment

```

conda env create -f environment.yml

conda activate linalg

```

## Resources

[fast.ai Computational Linear Algebra course](https://www.fast.ai/2017/07/17/num-lin-alg/)

[Numerical Linear Algebra by Lloyd N. Trefethen and David Bau III](https://www.amazon.com/Numerical-Linear-Algebra-Lloyd-Trefethen/dp/0898713617)

[Matrix Computations by Gene H. Golub and Charles F. Van Loan](https://www.amazon.com/Computations-Hopkins-Studies-Mathematical-Sciences/dp/1421407949)

[Iterative Methods for Sparse Linear Systems by Yousef Saad](https://www.amazon.com/Iterative-Methods-Sparse-Linear-Systems/dp/0898715342)