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We introduce Lineax, a library bringing linear solves and linear least-squares to the JAX+Equinox scientific computing ecosystem.
A generalized inverse for matrices
R. Penrose · 1955
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The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate
Gene H. Golub and V. Pereyra · 1973
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Digital Signal Processing
Alan V. Oppenheim and Ronald W. Schafer · 1975
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Matlab version: 9.13.0 (r2022b), 1984
The MathWorks Inc · 1984
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Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems
Youcef Saad and Martin H. Schultz · 1986
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Bi-cgstab: A fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems
H. A. van der Vorst · 1992
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Numerical Partial Differential Equations: Finite Difference Methods
J. W. Thomas · 1995
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Matrix Computations
Gene H. Golub and Charles F. Van Loan · 1996
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Numerical Linear Algebra
Lloyd N. Trefethen and David Bau · 1997
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Generalized Inverses: Theory and Applications
Adi Ben-Israel and Thomas N. E. Greville · 2003
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Numerical Optimization (Second Edition)
Jorge Nocedal and Stephen Wright · 2006
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Julia: A fresh approach to numerical computing
Jeff Bezanson, Alan Edelman, Stefan Karpinski, and Viral B Shah · 2017
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Jax: composable transformations of python+numpy programs, 2018
James Bradbury, Roy Frostig, Peter Hawkins, Matthew James, Johnson, Chris Leary, Dougal Maclaurin, George Necula, Adam Paszke, Jake VanderPlas, Skye Wanderman-Milne, and Qiao Zhang · 2018
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The deepmind jax ecosystem, 2020
Igor Babuschkin et al · 2020
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Highly accurate protein structure prediction with alphafold
John Jumper et al · 2021
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Brax - a differentiable physics engine for large scale rigid body simulation, 2021
C. Daniel Freeman, Erik Frey, Anton Raichuk, Sertan Girgin, Igor Mordatch, and Olivier Bachem · 2021
Optimal transport tools (ott): A jax toolbox for all things wasserstein
Marco Cuturi, Laetitia Meng-Papaxanthos, Yingtao Tian, Charlotte Bunne, Geoff Davis, and Olivier Teboul · 2022
Later among the works it cites.
Learning to correct spectral methods for simulating turbulent flows
Gideon Dresdner, Dmitrii Kochkov, Peter Norgaard, Leonardo Zepeda-Núñez, Jamie A. Smith, Michael P. Brenner, and Stephan Hoyer · 2022
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JAX-fluids: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows
Deniz A. Bezgin, Aaron B. Buhendwa, and Nikolaus A. Adams · 2023
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Linearsolve.jl: High-performance unified linear solvers, 2021
Chris Rackauckas et al · 2023
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Levanter — legible, scalable, reproducible foundation models with jax
David Hall, Ivan Zhou, and Percy Liang · 2023
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Decomposing reverse-mode automatic differentiation, 2021
Roy Frostig, Matthew J. Johnson, Dougal Maclaurin, Adam Paszke, and Alexey Radul · 2021
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On Neural Differential Equations
Patrick Kidger · 2021
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Equinox: neural networks in JAX via callable PyTrees and filtered transformations
Patrick Kidger and Cristian Garcia · 2021
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Flax: A neural network library and ecosystem for JAX, 2023
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Jake Vanderplas · 2023
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