class_14

class_14 - CS205 Class 14 Covered in class: 1, 3, 4...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
CS205 – Class 14 Covered in class: 1, 3, 4 Readings: 7.4, 8.1 to 8.3 Quadrature 1. Numerical quadrature approximate ( ) b a I f x dx for a given f a. These f ’s might be arbitrarily difficult to compute and only available by running a program. b. General approach : Subdivide [ , ] a b into n intervals 1 [ , ] i i x x with 0 x a and n x b and consider each subinterval separately 2. Newton-Cotes quadrature for each subinterval 1 [ , ] i i x x , choose n equally spaced points and use k-1 degree polynomial interpolation to approximate the integral a. Exact on polynomials of degree n-1 when n is even, as expected b. Exact on polynomials of degree n when n is odd, from symmetric cancellation i. c. local accuracy an exact method on k degree polynomials has a local error that scales like 2 ( ) k O h in each subinterval where h is the length of the subinterval d. global accuracy since there are   1 O h subintervals, the total error scales like 1 ( ) k O h i. doubling the number of subintervals, sends
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/05/2012 for the course CS 205A taught by Professor Fedkiw during the Fall '07 term at Stanford.

Page1 / 2

class_14 - CS205 Class 14 Covered in class: 1, 3, 4...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online