Smart systems in general, and specifically neural networks, are expected to be of great assistance in large scale matrix computation. However it was necessary to work with smaller problems at first step. To this end, a method based on using perceptrons and Kohonen networks for determining the first three modal frequencies of frames of up to 20 stories high and two bays wide from their stiffness and mass matrices, was developed. This paper introduces this modular network as a preferable alternative for designing smart systems for learning large scale mapping problems in structural engineering, and in addition, reports the successful application of this modular network to the Eigenvalue and modal frequency determination of shear frame structures.

This paper considers an inverse Eigenvalue problem for bisymmetric nonnegative matrices. We first discuss the specified structure of the bisymmetric matrices. Then for a given set of real numbers of order maximum five with special conditions, we construct a nonnegative bisymmetric matrix such that the given set is its spectrum. Finally, we solve the problem for arbitrary order n in the special case of the spectrum.

In this paper, the inverse Eigenvalue problem for the bordered diagonal matrices are reconsidered whose elements are equal to zero except for the first row, the first column and the diagonal elements. The necessary and sufficient conditions for existence of a symmetric bordered diagonal matrix from special spectral data have been determined. A new algorithm to make such matrices is derived and some numerical examples are given to illustrate the efficiency of the method.

In this research, we introduce an approach to , nd a family of sixth order Sturm-Liouville problems having the same spectrum. Using Darboux Lemma and the fact that any second order Sturm-Liouville problem with the Dirichlet boundary conditions is equivalent to a sixth order Sturm-Liouville problem, the considered problems are formulated.