| Abstract: | The problem of calculating the maximal singular number of a given real matrix is considered. The existing solution methods are briefly surveyed. A new optimization-type algorithm for computing the maximal singular number is suggested and substantiated. Its rate of convergence is proved to be linear. A relationship between the row sums of the matrix and one of its singular numbers is established, and new localization theorems are proved. It is shown how the suggested algorithm is related to the Relay relation relaxation method. Exceptional situations in which the algorithm converges to a non-maximal singular number are described. A computational trick for avoiding such situations with fairly high reliability is suggested. |
