# NUMERICAL ANALYSIS + MATLAB (Assignment)

only “one” page report

in the assignment attached, there is a demo for matlab

this is the demo:

Gaussian Elimination in floating point arithmetic

*((here is the code for this part for matlab)):

```% Class: MACM 316
% Title: Gaussian Elimination for a random matrix demo
% Description: Computes the mean solution error over Ntr trials for the
% system Ax=b where A is a random NxN matrix and x is a vector of ones.
% Plots the result as a histogram.
% File name: LSRandom.m

N = 10; % Matrix size
Ntr = 100; % Number of trials

errs = zeros(Ntr,1); % Vector of errors
x = ones(N,1); % exact solution vector

for i=1:Ntr

A = randn(N,N); % Construct a random NxN matrix (normally distributed)
b = A*x; % Compute the right-hand side vector
z = Ab; % Solve the linear system

errs(i) = max(abs(z-x)); % Compute the error
end

% Compute the mean and standard deviation of the error
mean_err = mean(errs)
sdev_err = sqrt(var(errs))

% Plot a histogram of the errors
hist(log10(errs),10)
title(['histogram of log_{10}(error) for ' num2str(Ntr) ' solves with a ' num2str(N) 'x' num2str(N) ' matrix'],'fontsize',14)
xlabel('log_{10}(error)','fontsize',12)
ylabel('number','fontsize',12)```