References¶

This page lists academic papers, books, and other resources related to Matrix Toolkit and test matrices.

Academic Papers¶

Anymatrix¶

[Higham2021]

Nicholas J. Higham and Mantas Mikaitis. Anymatrix: An Extendable MATLAB Matrix Collection. Numerical Algorithms, 90:3, 1175-1196, December 2021. DOI: 10.1007/s11075-021-01226-2

[HighamMikaitis2021Guide]

Nicholas J. Higham and Mantas Mikaitis. Anymatrix: An Extendable MATLAB Matrix Collection, Users’ Guide. MIMS EPrint 2021.15, Manchester Institute for Mathematical Sciences, The University of Manchester, UK. October 2021. URL: eprints.maths.manchester.ac.uk/2834

SuiteSparse Collection¶

[Davis2011]

Timothy A. Davis and Yifan Hu. The University of Florida Sparse Matrix Collection. ACM Transactions on Mathematical Software, 38:1, 2011. DOI: 10.1145/2049662.2049663

[Kolodziej2019]

Scott P. Kolodziej et al. The SuiteSparse Matrix Collection Website Interface. Journal of Open Source Software, 4(35):1244, 2019. DOI: 10.21105/joss.01244

Regularization¶

[Hansen1994]

Per Christian Hansen. Regularization Tools: A MATLAB Package for Analysis and Solution of Discrete Ill-Posed Problems. Numerical Algorithms, 6:1-35, 1994. DOI: 10.1007/BF02149761

[Hansen2010]

Per Christian Hansen, James G. Nagy, and Dianne P. O’Leary. Deblurring Images: Matrices, Spectra, and Filtering. SIAM, Philadelphia, 2006. DOI: 10.1137/1.9780898718874

Test Matrices¶

[Higham2002]

Nicholas J. Higham. Accuracy and Stability of Numerical Algorithms, Second Edition. SIAM, Philadelphia, 2002. DOI: 10.1137/1.9780898718027

[Gregory1993]

Robert T. Gregory and David L. Karney. A Collection of Matrices for Testing Computational Algorithms. Wiley-Interscience, 1969. ISBN: 978-0882756417

Books¶

Matrix Computations¶

[GolubVanLoan2013]

Gene H. Golub and Charles F. Van Loan. Matrix Computations, Fourth Edition. Johns Hopkins University Press, 2013. ISBN: 978-1421407944

[Trefethen1997]

Lloyd N. Trefethen and David Bau III. Numerical Linear Algebra. SIAM, Philadelphia, 1997. DOI: 10.1137/1.9780898719574

Sparse Matrices¶

[Saad2003]

Yousef Saad. Iterative Methods for Sparse Linear Systems, Second Edition. SIAM, Philadelphia, 2003. DOI: 10.1137/1.9780898718003

[DavisDirect]

Timothy A. Davis. Direct Methods for Sparse Linear Systems. SIAM, Philadelphia, 2006. DOI: 10.1137/1.9780898718881

Software and Packages¶

Python Packages¶

NumPy: Fundamental package for array computing
SciPy: Scientific computing library
ssgetpy: Python interface to SuiteSparse collection
PyTorch: Deep learning framework
JAX: Autograd and XLA
CuPy: NumPy-compatible GPU arrays

Online Resources¶

Websites¶

Documentation¶

Datasets¶

Matrix Collections¶

SuiteSparse: 2,800+ sparse matrices from real applications
Matrix Market: Collection of test matrices
Harwell-Boeing: Historic sparse matrix collection
NEP Collection: Nonlinear eigenvalue problems

Benchmarks¶

LINPACK: Linear algebra benchmarks
LAPACK: Linear Algebra PACKage benchmarks
HPL: High-Performance Linpack

Historical Notes¶

Test Matrices Evolution¶

The use of test matrices in numerical linear algebra has a rich history:

1960s: Early test matrices (Hilbert, Wilkinson)
1970s: Harwell-Boeing collection established
1990s: Matrix Market created by NIST
2000s: University of Florida collection (now SuiteSparse)
2020s: Anymatrix and modern test matrix frameworks

Citation¶

If you use Matrix Toolkit in your research, please cite:

@software{matrix_toolkit,
  title = {Matrix Toolkit: A Comprehensive Python Package for Matrix Collections},
  author = {Your Name},
  year = {2024},
  url = {https://github.com/yourusername/matrix-toolkit},
  version = {0.1.0}
}

For Anymatrix functionality, please also cite the original paper:

@article{higham2021anymatrix,
  title={Anymatrix: An Extendable {MATLAB} Matrix Collection},
  author={Higham, Nicholas J and Mikaitis, Mantas},
  journal={Numerical Algorithms},
  volume={90},
  number={3},
  pages={1175--1196},
  year={2021},
  publisher={Springer},
  doi={10.1007/s11075-021-01226-2}
}

License¶

Matrix Toolkit is distributed under the BSD 2-Clause License. See the LICENSE file for details.

Contributing¶

We welcome contributions! See <no title> for guidelines.

Acknowledgments¶

This project builds upon the work of many researchers and developers:

Nicholas J. Higham and Mantas Mikaitis for Anymatrix
Timothy A. Davis for SuiteSparse collection
Per Christian Hansen for Regularization Tools
The NumPy and SciPy development teams
All contributors to test matrix collections