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Inequality-Based Approximation of Matrix Eigenvectors

Kocsor A., Dombi J., Balint I.

International Journal of Applied Mathematics and Computer Science

2002

Vol. 12, no 4

533-538

A novel procedure is given here for constructing non-negative functions with zero-valued global minima coinciding with eigenvectors of a general real matrix A. Some of these functions are distinct because all their local minima are also global, offering a new way of determining eigenpairs by local optimization. Apart from describing the framework of the method, the error bounds given separately for the approximation of eigenvectors and eigenvalues provide a deeper insight into the fundamentally different nature of their approximations.