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The reconstruction of bordered- diagonal and Jacobi matrices from spectral data

โœ Scribed by Stephen E. Sussman-Fort

Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
477 KB
Volume
314
Category
Article
ISSN
0016-0032

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โœฆ Synopsis

Simple, new, direct methods are derived for constructing real, symmetric, bordered-diagonal and tridiagonaf matrices from their eigenvalues and the eigenvalues of any one of their principal submatrices.

A direct method is also presented for constructing, from its eigenvalues, a real tridiagonaf matrix which is symmetric about both its main and secondary diagonals.

The techniques described make use of special properties of positive, real, odd, rational functions which occur in electric circuit theory. Examples are given which demonstrate the various methods.

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## Abstract We consider the problem to reconstruct the mass distribution of a string where the mass is concentrated in a finite number of points, or, equivalently, the problem to reconstruct a simply connected mass spring system with unknown masses and stiffness parameters if the following data are