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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 25 - Effect of Small Pivots

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