We present a computational method for solving a class of boundary-value problems in Sturm-Liouville form. The algorithms are based on global polynomial collocation methods and produce discrete representations of the eigenfunctions. Error control is performed by evaluating the eigenvalue problem residuals generated when the eigenfunctions are interpolated to a finer discretization grid; eigenfun...

This paper introduces a novel spectral framework for solving Markov decision processes (MDPs) by jointly learning representations and optimal policies. The major components of the framework described in this paper include: (i) A general scheme for constructing representations or basis functions by diagonalizing symmetric diffusion operators (ii) A specific instantiation of this approach where g...

We show that a polynomial Hˆ(N) of degree N harmonic oscillator hamiltonian allows us to devise fully solvable continuous quantum system for which the first discrete energy eigenvalues can be chosen at will. In general such choice leads re-ordering associated eigenfunctions Hˆ number their nodes does not increase monotonically with increasing level number. Systems have certain ‘universal’ featu...

This study is on the fuzzy eigenvalues and fuzzy eigenfunctions of the Sturm-Liouville fuzzy problem with fuzzy eigenvalue parameter. We find fuzzy eigenvalues and fuzzy eigenfunctions of the problem under the approach of Hukuhara differentiability. We solve an example. We draw the graphics of eigenfunctions. We show that eigenfunctions are valid fuzzy functions or not.

Design optimization of structures with discrete and continuous search spaces is a complex optimization problem with lots of local optima. Metaheuristic optimization algorithms, due to not requiring gradient information of the objective function, are efficient tools for solving these problems at a reasonable computational time. In this paper, the Doppler Effect-Mean Euclidian Distance Threshold ...

This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all points, we define a diffusion distance between any two data points and show that the low dimensional representation of the data by the first few eigenvectors of th...

A framework for coherent pattern extraction and prediction of observables measure-preserving, ergodic dynamical systems with both atomic continuous spectral components is developed. This based on an approximation the generator system by a compact operator Wτ reproducing kernel Hilbert space (RKHS). The skew-adjoint, thus can be represented projection-valued measure, discrete compactness, associ...

This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Zn which are discrete analogs of the Schrödinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of the so-called pseudodifference operators (i.e...

Optimum design of structures is achieved while the design variables are continuous and discrete. To reduce the computational work involved in the optimization process, all the functions that are expensive to evaluate, are approximated. To approximate these functions, a semi quadratic function is employed. Only the diagonal terms of the Hessian matrix are used and these elements are estimated fr...