Survey of power, QR, and iterative methods for solution of largest eigenvalue of essentially positive matrices

Abstract

Abstract. Many of the popular methods for the solution of largest eigenvalue of essentially positive irreducible matrices are surveyed with the hope of finding an efficient method suitable for electromagnetic engineering, radiation problems, system identification problems, and solid mechanics. Eigenvalue computations are both fundamental and ubiquitous in computational science and its fast application areas. Some comparisons between several known algorithms, i.e. Power and QR methods, and earlier theory of Oepomo iterative techniques for solving largest eigenvalue of nonnegative irreducible matrices are presented since there is a continuing demand for new algorithm and library software that efficiently utilize and adapt to new applications.