# ENUME_Project1
A Numerical Method project cointaining 4 tasks.
## 1. 
Write a program finding macheps in the MATLAB environment on a lab computer or your
computer. 
## 2. 
Write a general program solving a system of n linear equations Ax = b using the indicated
method Apply the program to solve the system of linear equations for given matrix A and vector b, for increasing numbers
of equations n = 10,20,40,80,160,… until the solution time becomes prohibitive (or the
method fails), for:
### a) 
Aij { for i = j -> 13, for i = j-1 or i = j+1 -> 4, other -> 0 \
Bi = 2.4 + 0.6i, \
i,j = 1..n;
### b)
Aij = 4/[5(i + j – 1)], Bi = 1/(2 i), i – odd; Bi = 0, i – even, i, j = 1,…,n;

## 3
Write a general program for solving the system of n linear equations Ax = b using the
Gauss-Seidel and Jacobi iterative algorithms. Apply it for the system: \
13x1 + 2x2 – 8x3 + x4 =16 \
x1 + 10x2 + 5x3 – 2x4 = 24 \
6x1 + 2x2 – 23x3 + 15x4 = 184 \
x1 + 2x2 – x3 + 13x4 = 82

## 4
Write a program of the QR method for finding eigenvalues of 5×5 matrices: \
a) without shifts; \
b) with shifts calculated on the basis of an eigenvalue of the 2×2 right-lower-corner 
submatrix.