Mathematical algorithms – An Overview and Its Implementation

Mathematical algorithms are a class of algorithms that are used to solve mathematical problems, such as finding the root of an equation or solving a system of linear equations. Mathematical algorithms are used in a variety of fields, including engineering, physics, and finance.

One of the most basic mathematical algorithms is the Euclidean algorithm, which is used to find the greatest common divisor (GCD) of two numbers. The Euclidean algorithm works by repeatedly subtracting the smaller number from the larger number until one of the numbers becomes zero. The GCD is then the remaining number.

Another commonly used mathematical algorithm is the Newton-Raphson method, which is used to find the root of an equation. The Newton-Raphson method works by making an initial guess for the root and then iteratively improving the guess by using the slope of the function at that point.

The Gaussian elimination algorithm is another important mathematical algorithm. This algorithm is used to solve a system of linear equations. The Gaussian elimination algorithm works by representing the system of equations as a matrix and then performing a series of row operations to transform the matrix into row echelon form. The solution to the system of equations can then be found by back substitution.

The simplex algorithm is another important mathematical algorithm. This algorithm is used to solve linear programming problems, which involve maximizing or minimizing a linear objective function subject to linear constraints. The simplex algorithm works by starting with a basic feasible solution and then iteratively improving the solution by moving to adjacent vertices of the feasible region until the optimal solution is found.

In conclusion, mathematical algorithms are an important class of algorithms that are used to solve a wide range of mathematical problems. By understanding how these algorithms work and how they are implemented, we can develop efficient and effective solutions to problems in engineering, physics, finance, and other fields.