Numerical Analysis

This is the repository for scratch of Numerical Analysis with MATLAB.

Table of Contents

1. Roots of Equations

• Bisection Method
• Method of False Position
• Fixed Position Iteration
• Newton's Method
• Secant Method

2. Linear Equation

• Naive Gaussian Elimination

3. Optimizaiton

• Golden Section Search

1. Roots of Equations

- Bisection Method

main algorithm

while(1)
    xrold = xr;
    xr = (xl + xu) / 2;
    test = func(xl) * func(xr);
    if test < 0
        xu = xr;
    elseif test > 0
        xl = xr;

- Method of False Position

main algorithm

while(1)
    xrold = xr;
    fl = func(xl);
    fu = func(xu);
    xr = xu - fu * (xl - xu) / (fl - fu);
    test = fl * func(xr);
    if test < 0
        xu = xr;
    elseif test > 0
        xl = xr;

- Fixed Position Iteration

main algorithm

while(1)
    x1 = u;
    error = abs(x1 - x0);
    x0 = x1;
    u = func(x0);

- Newton's Method

main algorithm

while(1)
    x1 = x0 - u / v;
    error = abs(x1 - x0);
    x0 = x1;
    u = func(x0);
    v = df(x0);

- Secant Method

main algorithm

while(1)
    x = x1 - v * (x1 - x0) / (v - u);
    x0 = x1;
    u = v;
    x1 = x;
    v = func(x1);
    error  = abs(x1 - x0);

2. Linear Equation

- Naive Gaussian Elimination

3. Optimizaiton

- Golden Section Search