## ME209 Numerical Analysis

Direct Methods Gaussian Elimination Consider a system of three equations: $$ a_{11} x_1 + a_{12} x_2 + a_{13} x_3 = c_1 $$ $$ a_{21} x_1 + a_{22}

Direct Methods Gaussian Elimination Consider a system of three equations: $$ a_{11} x_1 + a_{12} x_2 + a_{13} x_3 = c_1 $$ $$ a_{21} x_1 + a_{22}

Taylor Series For a function \( f(x) \) where \( a \) is a solution. The difference between the initial guess \( x \) and the solution is denoted by \( \delta x \). \( f(x + \delta

Jacobi Iteration Method For a system $$ax_1 + bx_2 + cx_3 = A$$ Rearrange for each \( x \): $$x_1 = \frac{1}{a}(A -bx_2 -cx_3)$$ $$x_2 = \frac{

LU Decomposition A system of equations $$a_1x_1+b_1x_2+c_1x_3=A$$ $$a_2x_1+b_2x_2+c_2x_3=B$$ $$a_3x_1+b_