ALL YOU NEED IS LOVE

‘The tau-method is both an algorithm and a philosophy. It was invented by Cornelius Lanczos in the same paper (1938) that gave the world the pseudospectral method.’ - Chebyshev and Fourier Spectral Methods, John P. Boyd

Basic definition, important characteristics and some useful properties of some orthogonal polynomials.

Mikael Mortensen. A Generic and Strict Banded Spectral Petrov-Galerkin Method for Differential Equations with Polynomial Coefficients. SIAM J. Sci. Comput. 45 (2023).

A series of seminal papers by Jie Shen:
1.Direct Solvers for the Second and Fourth Order Equations Using Legendre Polynomials;
2.Direct Solvers for the Second and Fourth Order Equations Using Chebyshev Polynomials;
3.Polar and Cylindrical Geometries;
4.Spherical Geometries.

Sheehan Olver, Alex Townsend. A Fast and Well-Conditioned Spectral Method, SIAM Rev. 55 (2013)

Schwarz method, Optimal Schwarz method, Krylov Subspace methdod.

USTC24F Algebra Course (MATH5002P)
第三章 一般环上的模，群的表示，半单代数

USTC24F Advanced Real Analysis (MATH5001P) 广义函数初步

USTC24F Algebra Course (MATH5002P)
第二章 仿射代数几何初步，Gröbner基。

Introduction to pseudo-spectral methods, method of moments, least squares, and Galerkin method.