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Boyd "Chebyshev and Fourier Spectral Methods"http://depts.washington.edu/ph506/Boyd.pdf
Martinsson "Fast Direct Solvers for Elliptic PDEs"https://doi.org/10.1137/1.9781611976045
LeVeque "Finite difference methods for ordinary and partial differential equations"https://epubs.siam.org/doi/book/10.1137/1.9780898717839
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Johnson & Frigo "Implementing FFTs in Practice"https://github.com/mitmath/18336/blob/master/readings/johnson_frigo_implementing_ffts.pdf
Martinsson "The Hierarchical Poincare-Steklov (HPS) solver for elliptic PDEs: A tutorial"https://github.com/mitmath/18336/blob/master/readings/martinsson_poincare_steklov.pdf
Driscoll & Hale "Rectangular spectral collocation"https://doi.org/10.1093/imanum/dru062
Fortunato & Townsend "Fast Poisson solvers for spectral methods"https://arxiv.org/abs/1710.11259
Olver et al. "A Sparse Spectral Method on Triangles"https://doi.org/10.1137/19M1245888
Barnett et al. "A Parallel Nonuniform Fast Fourier Transform Library Based on an 'Exponential of Semicircle' Kernel"https://doi.org/10.1137/18M120885X
Fortunato et al. "The ultraspherical spectral element method"https://doi.org/10.1016/j.jcp.2020.110087
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Cipra "Top ten algorithms of the 20th century"https://github.com/mitmath/18336/blob/master/readings/siam_news_top_10_algorithms.pdf
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Martinsson "The Hierarchical Poincare-Steklov (HPS) solver for elliptic PDEs: A tutorial"https://github.com/mitmath/18336/blob/master/readings/martinsson_poincare_steklov.pdf
https://patch-diff.githubusercontent.com/mitmath/18336#lecture-7-introduction-to-spectral-methods
https://patch-diff.githubusercontent.com/mitmath/18336#lecture-8-fourier-spectral-methods-i
Vasil et al. "A new method for fast transforms in parity-mixed PDEs"https://github.com/mitmath/18336/blob/master/readings/vasil_parity_mixing.pdf
https://patch-diff.githubusercontent.com/mitmath/18336#lecture-9-fourier-spectral-methods-ii
Yeung & Ravikumar "Advancing understanding of turbulence through extreme-scale computation: Intermittency and simulations at large problem sizes"https://github.com/mitmath/18336/blob/master/readings/yeung_fourier_turbulence.pdf
https://patch-diff.githubusercontent.com/mitmath/18336#lecture-10-polynomial-interpolation
https://patch-diff.githubusercontent.com/mitmath/18336#lecture-11-chebyshev-collocation-methods
Driscoll & Hale "Rectangular spectral collocation"https://doi.org/10.1093/imanum/dru062
https://patch-diff.githubusercontent.com/mitmath/18336#lecture-12-dense-chebyshev-spectral-methods
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Olver & Townsend "A Fast and Well-Conditioned Spectral Method"https://doi.org/10.1137/120865458
https://patch-diff.githubusercontent.com/mitmath/18336#lecture-14-multidimensional-sparse-methods
Fortunato & Townsend "Fast Poisson solvers for spectral methods"https://arxiv.org/abs/1710.11259
https://patch-diff.githubusercontent.com/mitmath/18336#lecture-15-sparse-methods-for-curvilinear-domains
Vasil et al. "Tensor calculus in polar coordinates using Jacobi polynomials"https://doi.org/10.1016/j.jcp.2016.08.013
Vasil et al. "Tensor calculus in spherical coordinates using Jacobi polynomials. Part-I: Mathematical analysis and derivations"https://doi.org/10.1016/j.jcpx.2019.100013
Lecoanet et al. "Tensor calculus in spherical coordinates using Jacobi polynomials. Part-II: Implementation and examples"https://doi.org/10.1016/j.jcpx.2019.100012
https://patch-diff.githubusercontent.com/mitmath/18336#lecture-16-introduction-to-low-rank-methods
Townsend & Trefethen "Continuous analogues of matrix factorizations"http://dx.doi.org/10.1098/rspa.2014.0585
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Beatson & Greengard "A short course on fast mulitpole methods"https://github.com/mitmath/18336/blob/master/readings/beatson_greengard_fmm.pdf
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Martinsson's lectures from 2014 CBMS/NSF Conference on Fast Direct Solvershttp://amath.colorado.edu/faculty/martinss/2014_CBMS/lectures.html
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Martinsson's lectures from 2014 CBMS/NSF Conference on Fast Direct Solvershttp://amath.colorado.edu/faculty/martinss/2014_CBMS/lectures.html
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