├── LICENSE ├── README.md ├── 第 1 章_插值 ├── 三次样条插值 │ ├── 三次样条插值 │ │ ├── main.mlx │ │ └── myspline.mlx │ └── 三次样条插值（已知两端导数值） │ │ ├── cubic_spline_interpolation.mlx │ │ └── main.m ├── 分段低次插值多项式 │ ├── lagrange.mlx │ └── main.mlx ├── 分段线性插值 │ ├── linear_interpolation.m │ └── main.mlx ├── 埃尔米特插值 │ ├── elmit_interpolation.mlx │ └── main.mlx ├── 径向基函数插值 │ ├── 一维 │ │ └── main2.mlx │ └── 二维 │ │ └── main3.mlx └── 新建文件夹 │ ├── lagrange_interpolation.mlx │ ├── main.mlx │ └── newton_interpolation.mlx ├── 第 2 章_函数逼近 ├── 拟合类 │ └── 线性回归 │ │ └── main.mlx ├── 最佳一致逼近 │ ├── consistent_approximation.mlx │ └── main.mlx ├── 最佳平方逼近 │ ├── 利用勒让德多项式计算 │ │ └── main.mlx │ └── 利用希尔伯特矩阵计算 │ │ └── main.mlx └── 最小二乘法 │ ├── least_squares.mlx │ └── main.mlx ├── 第 3 章_数值积分与数值微分 ├── Gauss公式 │ ├── gauss.mlx │ └── main.mlx ├── Richardson 外推求微分 │ ├── Richardson.mlx │ ├── main.mlx │ └── 题目.png ├── 复合积分（化成多个小区间） │ ├── 复合Gauss求积公式 │ │ ├── gauss.mlx │ │ └── main.mlx │ ├── 复合梯形 │ │ ├── main.mlx │ │ └── trapezium.mlx │ ├── 复合辛普森(Simpon) 公式 抛物线法 │ │ ├── main.mlx │ │ └── simpson.mlx │ └── 矩形法 定积分定义 │ │ ├── main.mlx │ │ └── rectangle_solve.mlx ├── 牛顿-柯特斯(Newton-Contes)公式 │ ├── N_C.mlx │ └── main.mlx ├── 自适应积分 │ ├── 自适应梯形 │ │ ├── adapt_trapezium.mlx │ │ └── main.mlx │ └── 自适应辛普森 │ │ ├── adapt_Simpson.mlx │ │ └── main.mlx └── 龙贝格(Romberg)积分 │ ├── main.mlx │ └── romberg.mlx ├── 第 4 章_解线性方程组的直接办法 ├── Cholesky 分解 平方根法 │ ├── Cholesky_break_down.mlx │ ├── lu_solver.mlx │ └── main.mlx ├── Crout 分解 │ ├── Crout_solve.mlx │ └── main.mlx ├── 完全主元素消去法 │ ├── gauss.mlx │ └── main.mlx ├── 改进的平方根法 │ ├── Cholesky_improve_break_down.mlx │ ├── ldu_solver.mlx │ └── main.mlx ├── 直接三角分解法 杜立特尔Doolittle分解 LU 分解 │ ├── LU_solve.mlx │ └── main.mlx ├── 迭代改善法 + 高斯消元法 │ ├── gauss_round.mlx │ └── main.mlx ├── 追赶法 │ ├── catch_up.mlx │ └── main.mlx ├── 高斯列主元素消去法 │ ├── gauss.mlx │ └── main.mlx └── 高斯消去法 │ ├── gauss.mlx │ └── main.mlx ├── 第 5 章_解线性方程组的迭代方法 ├── gauss_seidel.mlx ├── jacobi.mlx ├── preconditioned_conjugate_gradient.mlx └── sor.mlx ├── 第 6 章_非线性方程与方程组的数值解法 ├── dichotomyMethod.mlx ├── fixedPointIteration.mlx ├── main.mlx ├── newtonMethod.mlx ├── parabolicMethod.mlx └── secantMethod.mlx ├── 第 7 章_常微分方程问题 ├── 单个方程 │ ├── eulerBackward.mlx │ ├── eulerExplicit.mlx │ ├── eulerImproved.mlx │ ├── eulerTrapezoidal.mlx │ ├── mian.mlx │ └── rungeKutta4.mlx └── 方程组 │ ├── eulerBackward.mlx │ ├── eulerExplicit.mlx │ ├── eulerImproved.mlx │ ├── eulerTrapezoidal.mlx │ ├── mian.mlx │ └── rungeKutta4.mlx └── 第 8 章_偏微分方程问题 ├── 双曲型方程 ├── 对流方程 │ └── main.mlx └── 波动方程 │ └── 均采用二阶中心差商 │ └── main.mlx └── 抛物型方程 └── 扩散方程 ├── Crank-Nicolson 法 └── main.mlx ├── 向前差分法 └── main.mlx └── 向后差分法 └── main.mlx /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2021 我不是wc 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # 数值分析代码 2 | 此代码用来配合数值分析课程使用。 3 | - 4 | ## 代码运行环境 5 | `MATLAB 2020a` 6 | ## 参考资料 7 | 1. 《数值分析 第五版》.李庆扬,王能超,易大义编著.清华大学出版社. 8 | 2. 《数值分析》原书第二版 .Timothy Sauer 著. 裴玉茹,马赓宇译. 机械工业出版社. 9 | ## 笔记 10 | 1. https://www.zhihu.com/column/c_1466717071224131584 11 | ## 我的联系方式 12 | CauZhangYang@outlook.com 13 | -------------------------------------------------------------------------------- /第 1 章_插值/三次样条插值/三次样条插值/main.mlx: -------------------------------------------------------------------------------- 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章_插值/三次样条插值/三次样条插值（已知两端导数值）/main.m: -------------------------------------------------------------------------------- 1 | clc,clear,close all 2 | x = 1:8; 3 | y = [0.84 0.91 0.14 -0.76 -0.96 -0.28 0.66 0.99]; 4 | n = length(x); 5 | u = rand; 6 | v = rand; 7 | xx = x(1):0.01:x(end); 8 | yy = cubic_spline_interpolation(x,y,xx,u,v); 9 | plot(x,y,'*') 10 | hold on 11 | plot(xx,yy,'LineWidth',1.5) 12 | h=legend('$(x_i,y_i)$','Three spline interpolation'); 13 | set(h,'Interpreter','latex','FontName','Times New Roman','FontSize',15,'FontWeight','normal') -------------------------------------------------------------------------------- /第 1 章_插值/分段低次插值多项式/lagrange.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/infinity-07/Numerical-analysis-code/72656a48958b8f6c1223d1eae2808cc8903fa24d/第 1 章_插值/分段低次插值多项式/lagrange.mlx -------------------------------------------------------------------------------- /第 1 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