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Elementary Numerical Analysis

Elementary Numerical Analysis. Instructor: Prof. Rekha P. Kulkarni, Department of Mathematics, IIT Bombay. This course introduces the implementation and analysis of numerical algorithms for finding an approximate solution to a mathematical problem. The important topics covered in this course are polynomial and piecewise polynomial (spline) interpolation, numerical integration and numerical differentiation, approximate solutions of differential equations, direct and iterative solution of a system of linear equations and eigenvalue problems. The theory behind various methods is rigorously discussed. Emphasis is on comparison of various methods and their implementation using a computer. (from nptel.ac.in)

Lecture 18 - LU Decomposition


Go to the Course Home or watch other lectures:

Lecture 01 - Introduction
Lecture 02 - Polynomial Approximation
Lecture 03 - Interpolating Polynomials
Lecture 04 - Properties of Divided Difference
Lecture 05 - Error in the Interpolating Polynomial
Lecture 06 - Cubic Hermite Interpolation
Lecture 07 - Piecewise Polynomial Approximation
Lecture 08 - Cubic Spline Interpolation
Lecture 09 - Tutorial 1
Lecture 10 - Numerical Integration: Basic Rules
Lecture 11 - Composite Numerical Integration
Lecture 12 - Gauss 2-point Rule: Construction
Lecture 13 - Gauss 2-point Rule: Error
Lecture 14 - Convergence of Gaussian Integration
Lecture 15 - Tutorial 2
Lecture 16 - Numerical Differentiation
Lecture 17 - Gauss Elimination
Lecture 18 - LU Decomposition
Lecture 19 - Cholesky Decomposition
Lecture 20 - Gauss Elimination with Partial Pivoting
Lecture 21 - Vector and Matrix Norms
Lecture 22 - Perturbed Linear System
Lecture 23 - Ill-Conditioned Linear System
Lecture 24 - Tutorial 3
Lecture 25 - Effect of Small Pivots
Lecture 26 - Solution of Nonlinear Equations
Lecture 27 - Quadratic Convergence of Newton's Method
Lecture 28 - Jacobi Method
Lecture 29 - Gauss-Seidel Method
Lecture 30 - Tutorial 4
Lecture 31 - Initial Value Problem
Lecture 32 - Multi-Step Methods
Lecture 33 - Predictor-Corrector Formula
Lecture 34 - Boundary Value Problems
Lecture 35 - Eigenvalues and Eigenvectors
Lecture 36 - Spectral Theorem
Lecture 37 - Power Method
Lecture 38 - Inverse Power Method
Lecture 39 - QR Decomposition
Lecture 40 - QR Method