Largest Eigenvalue Estimation of SPD Matrix
Let $A$ be a symmetric positive definite matrix, this application estimates its largest eigenvalue $\lambda_{\text{max}}$ using the method in [1]. It also finds the smallest eigenvalue $\lambda_{\text{min}}$ by applying the same method to the matrix $(1+\epsilon)\lambda_{\text{max}}I-A$, where $\epsilon > 0$. Minus the result to $(1+\epsilon)\lambda_{\text{max}}$ to get $\lambda_{\text{min}}$.
Note that this method is not expensive to implement and is for spd matrices only, if you are looking for a method for general dense real/complex matrices, Eigenvalue/Eigenvector Calculator is highly recommended.
Reference
- O'Leary, Dianne P., Stewart, G. W., and Vandergraft, James S. (1979), Estimating the Largest Eigenvalue of a Positive Definite Matrix, Mathematics of Computation, Vol. 33, pp. 1289–1292.
Input Data
See Input Data for how to enter data to a matrix and a vector of real numbers.