Mikael Mortensen. A Generic and Strict Banded Spectral Petrov-Galerkin Method for Differential Equations with Polynomial Coefficients. SIAM J. Sci. Comput. 45 (2023).
-
Efficient Spectral-Galerkin Method
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. -
The Ultraspherical Spectral Method
Sheehan Olver, Alex Townsend. A Fast and Well-Conditioned Spectral Method, SIAM Rev. 55 (2013)
-
Domain Decomposition Method
Schwarz method, Optimal Schwarz method, Krylov Subspace methdod.
-
半单代数与有限群表示
USTC24F Algebra Course (MATH5002P)
第三章 一般环上的模，群的表示，半单代数 -
Elementary of Distribution Theory
USTC24F Advanced Real Analysis (MATH5001P) 广义函数初步
-
仿射代数几何初步与Gröbner基
USTC24F Algebra Course (MATH5002P)
第二章 仿射代数几何初步，Gröbner基。 -
Weighted Residual Methods
Introduction to pseudo-spectral methods, method of moments, least squares, and Galerkin method.
-
Basic Harmonic Analysis
USTC24F Advanced Real Analysis (MATH5001P) 调和分析简介
1.Analysis on unit circle. 2.Analysis on Euclidean space. 3.Littlewood-Palay Theory. -
交换代数初步
USTC24F Algebra Course (MATH5002P)
第二章 Noether环和Noether模，Artin环和Artin模，局部化，整性，根式理想与准素理想。