assignment - Math 400 Assignment #1 -- Systems of Linear...

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Math 400 Assignment #1 -- Systems of Linear Equations 17 17 3 3 3 3 3 3 Find an approximate numerical solution to the system with 10 10 10 10 10 1 10 10 10 1 and = 1 1 10 10 2 1 1 1 10 3------ = Ax = b A b a) using basic Gaussian elimination b) using Gaussian elimination with partial pivoting c) using Gaussian elimination with (partially) scaled partial pivoting in each case compute the residual error vector . Compare your results for the three methods. For part a) try to find the precise step at which a large error is introduced. r = b - Ax 1. 2. In Gauss-Jordan Elimination the i th equation is used to eliminate the i th unknown from all of the equations except the i th. This is similar to Gaussian elimination, but in this method the augmented matrix for the linear system is reduced from A = x b [ ] (1) (1) (1) (1) 11 12 1 1 1 (1) (1) (1) (1) 21 22 2 2 1 (1) (1) (1) (1) 1 2 1 | n n n n n n n n nn a a a a a a a a A a a a a + + + = b (1) (1) 11 1 1 (2) (2) 22 2 1 ( ) ( ) 1 n n n n nn n n a a a a a a + + + to The solution is obtained by setting...
View Full Document

Page1 / 3

assignment - Math 400 Assignment #1 -- Systems of Linear...

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