We present new O(n3) algorithms that compute eigenvalues and eigenvectors to high relative accuracy in floating point arithmetic for the following types of matrices: symmetric Cauchy, symmetric diagonally scaled Cauchy, symmetric Vandermonde, and symmetric totally nonnegative matrices when they are given as products of nonnegative bidiagonal factors. The algorithms are divided into two stages: ...

In the ring of symmetric functions the inverse Kostka matrix appears as the transition matrix from the bases given by monomial symmetric functions to the Schur bases. We present both a combinatorial characterization and a recurrent formula for the entries of the inverse Kostka matrix which are different from the results obtained by Egecioglu and Remmel [ER] in 1990. An application to the topolo...

This chapter presents two fuzzy adaptive variable structure controllers for a class of uncertain multiinput multi-output nonlinear systems with actuator nonlinearities (i.e. with sector nonlinearities and dead-zones). The design of the first controller concerns systems with symmetric and positive definite control-gain matrix, while the design of the second one is extended to the case of non-sym...

In the MUSIC approach for multiple emitter location, the array covariance matrix is a Hermite matrix. In order to realize the MUSIC approach, we have to do the work of eigenvalue-based decomposition of the Hermite matrix. This paper proves that the problem of Hermite matrix decomposition can be transformed into the problem of real symmetric matrix decomposition, and the article gives the detail...

Gandin and Murphy have shown that if a skill score is linear in the scoring matrix, and if the scoring matrix is symmetric, then in the 2-event case there exists a unique, \equitable" skill score, namely the True Skill Score (or Kuipers' performance index). As such, this measure is treated as preferable to other measures because of its equitability. However, in most practical situations the sco...

The inverse C = [ci,j ] of an irreducible nonsingular symmetric tridiagonal matrix is a socalled Green’s matrix, i.e. it is given by two sequences of real numbers {ui} and {vi} such that ci,j = uivj for i ≤ j. A similar result holds for nonsymmetric matrices. An open problem on nonsingular sparse matrices is whether there exists a similar structure for their inverses as in the tridiagonal case....