An Inequality-based Approximation of Matrix Eigenvectors

András Kocsor¹, József Dombi², Imre Bálint³

¹Research Group on Artificial Intelligence University of Szeged,

²Department of Applied Informatics, University of Szeged,

³Department of Theoretical Physics, University of Szeged,
Department of Pharmaceutical Analysis, University of Szeged,
Department of Natural Sciences, Dunaújváros Polytechnic,

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 for the determination of eigenpairs by local optimization. Beyond 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.