This repository contains Python implementations of various numerical analysis methods. These methods are commonly used for solving mathematical problems and finding approximate solutions to equations and systems of equations. These implemenations are based off the theory I learnt in the Numerical Analysis course at BITS, Pilani.
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A root-finding method that repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing.
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Regular Falsi Method / Method of False Position:
A root-finding algorithm that computes a succession of roots based on linear interpolation.
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A root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function.
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Newton Method:
An iterative method for finding successively better approximations to the roots (or zeroes) of a real-valued function.
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Newton Method for Multiple Roots:
Extension of Newton's method for finding multiple roots of a function.
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Method of Iteration:
A method that repeatedly applies a function to an initial guess until a desired accuracy is reached.
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Newton Method for System of Nonlinear Equations:
An extension of Newton's method for solving systems of nonlinear equations.
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Muller's Method:
A root-finding algorithm which combines bisection, secant, and inverse quadratic interpolation methods.
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Gauss Elimination Method (Partial Pivoting):
A method for solving systems of linear equations by transforming the augmented matrix into upper triangular form through row operations.
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Gauss Jordan Method (Partial Pivoting):
An extension of Gauss elimination method which transforms the augmented matrix into reduced row-echelon form.
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LU Decomposition Method:
A method for solving systems of linear equations by decomposing the matrix into lower and upper triangular matrices.
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Gauss Jacobi Method:
An iterative method for solving systems of linear equations by successively improving the solution approximation.
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Gauss Seidel Method:
An iterative method similar to Gauss Jacobi method but with a more efficient approach by utilizing newly updated values.