数值计算方法实习报告1.doc

数值计算方法实习报告实验一1、只留导电介质的数值模拟2、污染扩散问题的数值模拟实验二1、线性最小二乘的数据拟合 2、非线性最小二乘的数据拟合 以下是用有理函数和光滑样条对铜的热膨胀系数和温度进行拟合3.插值的数据拟合以下是用三次样条和简单函数拟合数据：x= 0:0.05:2; y = x .* sin(1./(x+eps)相关代码： cftool load hahn1 x=0:0.05:2; y=x.*sin(1./(x+eps);结果如下：实习三 基于偏微方程（PDE）的图像降噪和还原代码：% TV demo % Based on: ROF92 L. Rudin, S. Osher, E. Fatemi,% Nonlinear Total Variation based noise removal algorithms,% Physica D 60 259-268,1992.% Simple TV denoising %I = imread(1.jpg); % load imageI = double(I(16:270,16:270); % cut a piece, convert to double% paramsiter = 80;% dt=0.2; eps=1;% Add noisestd_n = 20; % Gaussian noise standard deviationIn = randn(size(I)*std_n; % White Gaussian noiseI0 = I + In; % noisy input image% show original and noisy imagesclose allfigure(1); imshow(uint8(I); title(Original)figure(2); imshow(uint8(I0); title(Noisy image)% denoise image by using tv for some iterationsJ = tv(I0,iter);figure(3); imshow(uint8(J); title(Denoised image)% TV denoising with (scalar) data fidelity term % Here we assume the noise vaiance is known.% Therefore we can compute lambda (instead of fixing% iter). TV therfore can run automatically quite well.% The process is slower.J = I0;% paramsep_J = 0.01; % minimum mean change in image Jlam = 0; J_old = 0;iter = 10; dt = 0.2; eps = 1;18var_n = std_n2; % noise variancei = 0;while (mean(mean(abs(J - J_old) ep_J), % iterate until convergenceJ_old = J;J = tv(J,iter,dt,eps,lam,I0); % scalar lamlam = calc_lam(J,I0,var_n,eps); % update lambda (fidelity term)end % f