数值分析的MATLAB程序设计new

1、数值分析作业题目 利用MATLAB编写数值算法程序 班级 / 学号 04140101/20100414028学 生 姓 名 张阳 指 导 教 师 刘勇进 一、 编写lagrange插值法计算拉氏基函数，再求和。图 1 拉氏基函数求解流程图Lagrange_base_function.m文件%Copyright(c) 2012 ShenYang Areospace University%All rights reserved%file name :Lagrange_base_function.m%summary :%current edition :%programmer :Yung Zhung

2、%accomplish time :2012-04-15%function name :Lagrange_base_function.m%function describe :%function in detailed :%function Y = Lagrange_base_function(x, k)n = length(x);y = ones(n, 2);Y = 1;for ii = 1 : n if ii = k continue; end y(ii, 2) = -x(ii); Y = conv(Y, y(ii, :);endend图 2 计算lagrange插值函数及差值值Lagra

3、nge.m文件%Copyright(c) 2012 ShenYang Areospace University%All rights reserved%file name :Lagrange.m%summary :%current edition :%programmer :Yung Zhung%accomplish time :2012-04-15%function name :Lagrange.m%function describe :%function in detailed :%function Y = Lagrange(x, y, point)if min(size(x) 1 | m

4、in(size(y) 1 error(the muxt be two vectors!);endn = length(x);if n = length(y) error(the dimention of the two vectors must aggree!);endY = 0;for ii = 1 : n y_1 = Lagrange_base_function(x, ii); Y = polyadd(Y, y(ii) * y_1 / polyval(y_1, x(ii);endif nargin = 2 disp(Y);else Y = polyval(Y, point);end二、 编

5、写复合二重simpson求积公式图 3 二重复合simpson公式流程图转化为一重simpson求积公式。%Copyright(c) 2012 ShenYang Areospace University%All rights reserved%file name :simpson_con.m%summary :%current edition :%programmer :Yung Zhung%accomplish time :2012-06-25%function name :simpson_con.m%function describe :%function in detailed :%fu

6、nction val = simpson_con(f, a, b, c, d, m, n)if b a flag_1 = a; a = b; b = flag_1; flag_1 = -1;else flag_1 = 1;endif d c flag_2 = d; d = c; c = flag_2; flag_2 = -1;else flag_2 = 1;endh_1 = (b - a) / m;h_2 = (d - c) / n;x_1 = a : h_1 / 2 : b;x_2 = c : h_2 / 2 : d;x_1, x_2 = meshgrid(x_1, x_2);y = f(x

7、_1, x_2);y_1 = (y(1, :) + y(2 * n + 1, :) + 2 * sum(y(3 : 2 : 2 * n - 1, :) + 4 * sum(y(2 : 2 : 2 * n, :) / 6 * h_2;val = (y_1(1) + y_1(2 * m + 1) + 2 * sum(y_1(3 : 2 : 2 * m - 1) + 4 * sum(y_1(2 : 2 : 2 * m) / 6 * h_1 * flag_1 * flag_2;end三、 编写Gauss消去法图 4 求解Gauss消去法Gauss_01.m文件%Copyright(c) 2012 Sh

8、enYang Areospace University%All rights reserved%file name :Gauss_01.m%summary :%current edition :%programmer :Yung Zhung%accomplish time :2012-06-14%function name :Gauss_01.m%function describe :%function in detailed :%function A = Gauss_01(A)n = size(A, 1);if n = size(A, 2) error(error!);endfor ii = 1 : n - 1 %for jj = ii + 1 : n % A(jj, ii : n) = A(jj, ii : n) - A(ii, ii : n)