MATLAB Code Implementation for Function Approximation

This program contains multiple algorithms for function approximation in MATLAB. The implemented algorithms include:

- Chebyshev Algorithm: Approximates known functions using Chebyshev polynomials, which provide excellent convergence properties and minimize maximum error through orthogonal polynomial basis functions

- Legendre Algorithm: Utilizes Legendre polynomials for function approximation, employing orthogonal polynomials that are particularly effective for problems defined on symmetric intervals

- Pade Algorithm: Implements rational function approximation using Pade approximants, which often provide better approximation than polynomial methods for functions with singularities

- Remez Algorithm (lmz): Determines the optimal uniform approximation polynomial using the Remez exchange algorithm, which iteratively finds the minimax solution

- ZJPF Algorithm: Computes the optimal mean square approximation polynomial by minimizing the integral of squared errors, typically implemented using orthogonal polynomial projections

- Fourier Algorithm (FZZ): Approximates known continuous periodic functions using Fourier series expansion, implementing spectral methods for periodic boundary conditions

These algorithms provide comprehensive tools for accurately approximating target functions, enhancing program precision and utility across various mathematical and engineering applications.