An overview of Clenshaw–Curtis and Gauss quadrature methods for numerical integration, as well as the computation of quadrature nodes and weights.
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Clenshaw Algorithm
A brief introduction to Clenshaw algorithm for evaluating orthogonal polynomial expansions.
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动物凶猛
那时候好像永远是夏天，太阳总是有空出来伴随着我。阳光充足，太亮，使得眼前一阵阵发黑。
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Jacobi Matrices
Jacobi matrices represent a cornerstone binding two wings of the same building: One is built from moments, continued fractions, and polynomials, with the purpose of approximating functions and integrals. The other is built from vectors, vector spaces, operators, and matrices with the purpose of matrix computations such as solving linear algebraic systems and approximating eigenvalues.
– Krylov Subspace Methods - Principles and Analysis -
Optimization Algorithms - Dual Algorithms & ALM & ADMM & BCD
USTC 2025 Spring Semester Course Notes for Optimization Algorithms.
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Optimization Algorithms - Newton's Methods
USTC 2025 Spring Semester Course Notes for Optimization Algorithms.
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Optimization Algorithms - Gradient Methods
USTC 2025 Spring Semester Course Notes for Optimization Algorithms.
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Basic Theory of Optimization Algorithms
USTC 2025 Spring Semester Course Notes for Optimization Algorithms.
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Numerical Methods for Nonlinear Equations
USTC 2025 Spring Semester Course Notes for Numerical Methods for Nonlinear Equations, including basic numerical methods e.g. finite volume method with Godunov’s flux, high order Godunov’s flux, Lax-Friedrichs flux, TVD/TVB limiter, and WENO method etc.
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Theory of Nonlinear Equations
USTC 2025 Spring Semester Course Notes for Numerical Methods for Nonlinear Equations, including the basic theory of nonlinear equations, e.g. weak solution, shock waves, rarefaction waves, contact discontinuities, Riemann problem, Rankine-Hugoniot condition, entropy solution, etc.