# Numerical Analysis/Householder transformation exercises

# Householder's method Exercises[edit | edit source]

## Exercise 1[edit | edit source]

This exercise will help you in introducing how to perform the Householder's method to transform a symmetric matrix A into the tridiagonal form. All of the notations and computations in this Exercise follow from those in Section 9.3, *Numerical Analysis*, Burden and Faires, 8th Edition. It's recommended that you read that section before solving the problem. It's also recommended that you read the following useful links

1. *Householder's method for symmetric matrices*, J. H. Wilkinson, Handbook Series Linear Algebra, Volume 4, Number 1 / December, 1962, Springer Berlin / Heidelberg.

2. *Module for Householder Transformations*, Mathematics Department, California State University, Fullerton.

**Problem**

Let

Perform Householder's method to bring A into a tridiagonal form.
**Solution**
**Step 1: k = 1** (Meaning: Making 0's for the third and fourth rows of the first column)

**Step 2: k = 2** (Meaning: Making 0's for the fourth row of the second column)

In Step 2, we redo the computations in Step 1 with the matrix

Now the matrix is in a tridiagonal form. The Householder's method is complete.

## Exercise 2[edit | edit source]

## Exercise 3[edit | edit source]

**Problem**

Based on the computations performed in Exercise 1, write code in Matlab to perform the Householder's method for an input symmetric matrix A.

**Solution**

132.235.39.18 19:02, 28 May 2009 (UTC) Nam Nguyen