Scientific Computing

This module demonstrates QR iteration with shifts for computing all
the eigenvalues and eigenvectors of a matrix. Starting with a given
matrix, the QR
factorization of the current matrix is computed at each iteration,
the new matrix is then given by the reverse product
*R*** Q** of the

The user first selects a matrix size, then selects a matrix by choosing
a preset example, a random matrix, or typing desired entries into the
array on the left. The successive steps of QR iteration are then
carried out sequentially by repeatedly clicking on NEXT or on the
currently highlighted step. At each iteration, the user can select the
Rayleigh quotient shift, the Wilkinson shift, or can enter any desired
value for the shift. Changes in the matrix are shown in the array on
the left, while the two arrays on the right show the computed
** Q** and

**Reference:** Michael T. Heath, *Scientific Computing,
An Introductory Survey*, 2nd edition, McGraw-Hill, New York,
2002. See Section 4.5.6, especially Algorithm 4.8 and Example 4.16.

**Developers:** Jeffrey Naisbitt and Michael Heath