The aim of the course was to familiarize student with ; Errors in summation, stability in numerical analysis. Linear algebraic equations: Gaussian elimination, direct triangular decomposition, matrix inversion, SVD. Root-finding: review of bisection method, Newton's method and secant method; real roots of polynomials, Laguerre's method. Matrix eigenvalue problems: Power method, eigenvalues of real symmetric matrices using Jacobi method, applications. Interpolation theory: Polynomial interpolation, Newton's divided differences, forward differences, interpolation errors, Hermite interpolation, cubic splines. Approximation of functions: Taylor's theorem, remainder term; Least squares approximation problem, Orthogonal polynomials, Near minimax approximation. Numerical integration: review of trapezoidal and Simpson's rules, Newton – Cotes integration formulas, Gaussian quadrature; Error estimation. Numerical differentiation. Random numbers; Monte Carlo method.
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📄 Programs for linear regression and simulations [https://drive.google.com/drive/folders/10vac-RgnduznuY5WmAWSgc3v41z5Xk7L?usp=sharing)
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📫 Reach me [email protected]