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.
Perform Householder's method to bring A into a tridiagonal form.
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]
Based on the computations performed in Exercise 1, write code in Matlab to perform the Householder's method for an input symmetric matrix A.
220.127.116.11 19:02, 28 May 2009 (UTC) Nam Nguyen