Homework5

# Homework5 - Department of Mathematics University of Houston...

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

University of Houston Numerical Analysis I Dr. Ronald H.W. Hoppe Numerical Analysis I (5th Homework Assignment) Exercise 17 ( Reformulation of linear least squares problems ) Let A R m × n , m > n, rank A = n, b R m . The linear least squares problem ( * ) k Ax - b k 2 = min can be formulated as the linear algebraic system ( ** ) ˆ I m A A T 0 ! ˆ r x ! = ˆ b 0 ! , where I m stands for the m × m unit matrix and r := b - Ax R m is the residual. (i) Using the normal equations, show that the component x of the solution of ( ** ) solves the linear least squares prolem ( * ). (ii) Given a decomposition of A according to ( ) A = Q ˆ R 0 ! with an orthogonal matrix Q R m × m and a regular upper triangular matrix R R n × n show that by orthogonal row and column transformations the linear system ˆ I m A A T 0 ! ˆ p z ! = ˆ f g ! can be transformed to the form I n 0 R 0 I m - n 0 R T 0 0 h d z = f

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/21/2012 for the course ENG 3000 taught by Professor Staff during the Spring '12 term at University of Houston.

### Page1 / 3

Homework5 - Department of Mathematics University of Houston...

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

View Full Document
Ask a homework question - tutors are online