Numerical_Analysis

Numerical Techniques, All Implemented from scratch in Python

1. Root Finding Algorithms for f(x)=0 :

1. Bisection Method
2. Secant Method
3. Regula-Falsi Method
4. Newton-Raphson Method
5. Birge-Vieta Method
6. Bairstow's Method

• Functions can be any algebraic combinations of polynomials Pn(x), exp(x), pi, log2(x),log10(x), acos(x), asin(x) ,atan(x) , cos(x) ,sin(x), tan(x), acosh(x),asinh(x),atanh(x),cosh(x), sinh(x), tanh(x) ,gamma(x), lgamma(x)
• All algorithms have independent implementations.
• The iterative_methods.py file has all algorithms together, and can compare performance and convergence of all these methods.
• Also implemented pretty printing for all functions, so functions can be printed in their mathematical notational form within the terminal.

Dependencies: Python 2.7, Numpy 1.16.1, Sympy 1.3

2. Matrix Decomposition Algorithms :

1. LU Decomposition
   a) Doolittle Method, L[i,i]=1, Implemented in O(nxn)
   b) Crout's Method, U[i,i]=1, Implemented in O(nxn)
2. L(L.T) Decompostion
   a) Cholesky's Method

• All algorithms have independent implementations.
• The decomposition.py file has all algorithms together, and can compare performance and convergence of all these methods.

Dependencies: Python 3.6.7, Numpy 1.16.1

3. Matrix Equation Solvers for Ax=b :

1. Gauss-Jacobi Method
2. Gauss-Seidel Method

• All algorithms have independent implementations.
• The solving_matrix_equations.py file has all algorithms together, and can compare performance and convergence of methods.

Dependencies: Python 3.6.7, Numpy 1.16.1

4. Matrix Inversion

• O(n^3) Algorithm.
• Prints the inverse of the matrix if it is invertible, 'INVALID' otherwise. Also handles 0 pivot and NaN exceptions.

Dependencies: E