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A note on a collection of papers on spectral approximation of convolution operators.

1. Xu, K., Austin, A. P., & Wei, K. (2017). A fast algorithm for the convolution of functions with compact support using Fourier extensions. SIAM Journal on Scientific Computing.
2. Xu, K., & Loureiro, A. F. (2018). Spectral approximation of convolution operators. SIAM Journal on Scientific Computing.
3. Loureiro, A. F., & Xu, K. (2019).Volterra-type convolution of classical polynomials. Mathematics of Computation.
4. Liu, X., Deng, K., & Xu, K. (2024). Spectral approximation of convolution operators of Fredholm type. SIAM Journal on Scientific Computing.

In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of an orthonormal matrix Q and an upper triangular matrix R. QR decomposition is often used to solve the linear least squares (LLS) problem and is the basis for a particular eigenvalue algorithm, the QR algorithm.

With the help of the FFT, we can compute the forward and backward Chebyshev transform in O(N log(N)) operations.

Gauss-type quadratures are a class of quadrature rules that approximate the integral of a function by a weighted sum of the function values at certain points.

Brief introduction to fractional derivatives and integrals.

To the Lighthouse is a novel by Virginia Woolf. The novel centres on the Ramsay family and their visits to the Isle of Skye in Scotland between 1910 and 1920.

国境の長いトンネルを抜けると雪国であった。夜の底が白くなった。信号所に汽車が止まった。

一切都不会过去。 — 契诃夫

Many classic iterative methods are based on subspace projection, i.e., krylov subspace methods for solving sparse linear systems, including the Conjugate Gradient (CG) method, the Generalized Minimal Residual (GMRES) method, the BiConjugate Gradient Stabilized (BiCGSTAB) method, and the Preconditioned Conjugate Gradient (PCG) method.

Scientific computing has traditionally required the highest performance, yet domain experts have largely moved to slower dynamic languages for daily work. We believe there are many good reasons to prefer dynamic languages for these applications, and we do not expect their use to diminish … The Julia programming language fills this role: it is a flexible dynamic language, appropriate for scientific and numerical computing, with performance comparable to traditional statically-typed languages. — Julia Documentation