This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Homework 3 Foundations of Computational Math 1 Fall 2010 The solutions will be posted on Wednesday, 9/22/09 Problem 3.1 Suppose A R n n is a nonsymmetric nonsingular diagonally dominant matrix with the following nonzero pattern (shown for n = 6) * * * * * * * * 0 0 0 0 * * 0 0 0 * 0 0 * 0 0 * 0 0 0 * * 0 0 0 0 * It is known that a diagonally dominant (row or column dominant) matrix has an LU factor ization and it can be computed stably without pivoting. 3.1.a . Describe an algorithm that solves Ax = b as efficiently as possible. 3.1.b . Given that the number of operations in the algorithm is of the form Cn k + O ( n k 1 ), where C is a constant independent of n and k > 0, what are C and k ? Problem 3.2 It is known that if partial or complete pivoting is used to compute PA = LU or PAQ = LU of a nonsingular matrix then the elements of L are less than 1 in magnitude, i.e.,  ij  1....
View
Full
Document
This note was uploaded on 07/25/2011 for the course MAD 5403 taught by Professor Gallivan during the Spring '11 term at University of Florida.
 Spring '11
 Gallivan

Click to edit the document details