Scientific Computing

This module demonstrates power iteration and inverse iteration for computing an eigenvector corresponding to the largest or smallest eigenvalue, respectively, of a matrix. An arbitrary nonzero starting vector is multiplied repeatedly by the matrix (or its inverse). To avoid overflow or underflow, the resulting new vector is rescaled at each iteration to have ∞-norm 1.

The user first chooses a 2 × 2 symmetric matrix, either by typing
in its entries or by selecting a random or preset example. Normalized
eigenvectors of the matrix are shown by arrows on the plot, with a dark
arrow corresponding to the larger eigenvalue (in magnitude) and a light
arrow corresponding to the smaller eigenvalue. The user then selects a
starting vector by clicking on the plot, and selects either power
iteration or inverse iteration. The successive steps of the
corresponding algorithm are then carried out sequentially by repeatedly
clicking on NEXT or on the currently highlighted step. If power
iteration is selected, then the starting vector ** x** is
multiplied by the matrix

**Reference:** Michael T. Heath, *Scientific Computing,
An Introductory Survey*, 2nd edition, McGraw-Hill, New York,
2002. See Sections 4.5.1 and 4.5.2, especially Figure 4.3 and Examples
4.10-4.12.

**Developers:** Nicholas Exner, Michael Heath, and Jeffrey Naisbitt