of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy NEW OPTIMIZATION METHODS AND APPLICATIONS IN KERNEL-BASED MACHINE LEARNING By Onur Şeref December 2006 Chair: Panos M. Pardalos Major Department: Industrial and Systems Engineering In this study, new optimization methods are introduced o...

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This paper constitutes a first step towards an extension of correspondence analysis with fuzzy data (FCA). At this stage, our main objective is to lay down the algebraic foundations for this fuzzy extension of the usual correspondence analysis. A two-step method is introduced to convert the fuzzy eigenvalue problem to an ordinary one. We consider a fuzzy matrix as the set of its cuts. Each such...

We develop lowest-order asymptotic approximations for the eigenfrequencies and eigenfunctions of linear, isentropic, low-frequency g-modes in stars consisting of a convective core and radiative envelope. The approximations are derived from a fourth-order system of differential equations in the divergence and radial component of the Lagrangian displacement without neglecting the Eulerian perturb...

The initial aim of the present paper is to provide a complete description for the eigenvalue problem of the non-commutative harmonic oscillator (NcHO), which is given by a two-by-two system of paritypreserving ordinary differential operator [19], in terms of Heun’s ordinary differential equations, the second order Fuchsian differential equations with four regular singularities in a complex doma...

We put forward a new method for the solution of eigenvalue problems for (systems of) ordinary differential equations, where our main focus is on eigenvalue problems for singular Schrödinger equations arising for example in electronic structure computations. In most established standard methods, the generation of the starting values for the computation of eigenvalues of higher index is a critica...