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Numerical Methods and Computation. Instructor: Prof. S. R. K. Iyengar, Department of Mathematics, IIT Delhi. This course derives and analyzes numerical methods for the solution of various problems.
1138 years, 9 months
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The course discusses the numerical solution of nonlinear system of algebraic equations. It will construct methods for finding the roots or zeros of a transcendental or a polynomial equation in one variable. Then it will extend the methods for the solution of a system of nonlinear equations. The course will consider a data or a table of values and construct the polynomial that fits this data exactly. This polynomial can be used for interpolating or predicting the value of the function, represent the data at any intermediate point. This polynomial may also be used for various other operations like differentiation and integration. In approximation the course will deal with approximation to a continuous function or to a function which represents the given data. Finally, the course will use the interpolating polynomial of a given data to find the derivative of a function, and construct methods to numerically integrate a given function or to integrate a function that represents a given data. (from nptel.ac.in)
Course Currilcum
- Lecture 01 – Errors in Computation and Numerical Instability Unlimited
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- Lecture 02 – Methods for Finding the Root: Bisection Method Unlimited
- Lecture 03 – Regula Falsi Method, Newton-Raphson Method, Chebyshev Method Unlimited
- Lecture 04 – Muller’s Method, Multipoint Iteration Methods, Convergence of the Secant Method Unlimited
- Lecture 05 – Rate of Convergence of the Secant Method, General Iteration Method Unlimited
- Lecture 06 – Finding the Multiple Roots of Nonlinear Equations: Newton-Raphson Method Unlimited
- Lecture 07 – Polynomial Equations: Sturm Sequences, Sturm’s Theorem Unlimited
- Lecture 08 – Polynomial Equations: Birge Vieta Method Unlimited
- Lecture 09 – Polynomial Equations: Bairstow Method Unlimited
- Lecture 10 – Polynomial Equations: Graeffe’s Root Squaring Method Unlimited
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- Lecture 11 – Introduction to Solution of a System of Linear Algebraic Equations Unlimited
- Lecture 12 – Direct Methods: Gauss Elimination Method Unlimited
- Lecture 13 – Gauss Elimination Method with Partial Pivoting, Gauss-Jordan Method Unlimited
- Lecture 14 – LU Decomposition Unlimited
- Lecture 15 – Cholesky Method (Square Root Method), Partition Method Unlimited
- Lecture 16 – Examples of Finding the Inverse Matrix using Partition Method Unlimited
- Lecture 17 – Iteration Methods: Jacobi Method, Gauss-Seidel Method Unlimited
- Lecture 18 – Generalization of the Gauss-Seidel Method, Norm of a Matrix Unlimited
- Lecture 19 – Matrix Norms, Convergence of Iterative Methods, Optimal Relaxation Factor Unlimited
- Lecture 20 – Determining Optimal Relaxation Factor, Eigenvalue Problems, Gershgorin Circles Unlimited
- Lecture 21 – Finding the Eigenvalues and the Corresponding Eigenvectors: Jacobi Method Unlimited
- Lecture 22 – Finding the Eigenvalues and the Corresponding Eigenvectors: Givens Method Unlimited
- Lecture 23 – Finding the Eigenvalues of an Arbitrary Matrix: Rutishauser Method Unlimited
- Lecture 24 – Eigenvalue Problems: Power Method, Convergence of the Power Method Unlimited
- Lecture 25 – Introduction to Interpolation and Approximation Unlimited
- Lecture 26 – Lagrange Interpolating Polynomial, Error of Interpolation Unlimited
- Lecture 27 – Error of Interpolation (cont.), Divided Differences Unlimited
- Lecture 28 – Newton’s Divided Difference Interpolating Polynomial, Forward/Backward Differences Unlimited
- Lecture 29 – Newton’s Forward/Backward Difference Formula Unlimited
- Lecture 30 – Hermite Interpolating Polynomial, Definition of Approximation, Error Norms Unlimited
- Lecture 31 – Least Squares Approximation Unlimited
- Lecture 32 – Quadratic Approximation, Uniform Approximation Unlimited
- Lecture 33 – Chebyshev Polynomial Approximation Unlimited
- Lecture 37 – Numerical Integration: Newton-Cotes Formula Unlimited
- Lecture 38 – Trapezoidal Rule, Simpson’s Rule Unlimited
- Lecture 39 – Gauss-Legendre 2-point and 3-point Formula Unlimited
- Lecture 40 – Gauss-Chebyshev Formula Unlimited
- Lecture 41 – Gauss-Hermite Quadrature Rules Unlimited
