Media Summary: Introducing interpolation using Lagrange polynomials and divided differences. OIT Math 451 section 4.3a: Numerical Differentiation I Introduction of the nature of numerical solutions to non-linear equations, solving one at a time.
Oit Math 451 Session 4 - Detailed Analysis & Overview
Introducing interpolation using Lagrange polynomials and divided differences. OIT Math 451 section 4.3a: Numerical Differentiation I Introduction of the nature of numerical solutions to non-linear equations, solving one at a time. Introduction of linear systems of equations using a fictional electronics manufacturing example. Newton's approach to polynomial interpolation. How simple arithmetic operations, particularly subtraction, can cause loss of significant digits, and damage to the results.
Improving the first order method by making use of multiple stages and locations Developing the Newton-Raphson Method to find a root of a single non-linear equation. Part 2 of Newton's interpolation method. This approach recursively build interpolative polynomials of increasing order to fit (x,y) ... Applying the classic definition of a definite integral to a numerical method which we will call the rectangular rule.
