In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...

“Kriging” is the name of a parametric regression method used by hydrologists and mining engineers, among others. Features of the kriging approach are that it also provides an error estimate and that it can conveniently be employed also to estimate the integral of the regression function. In the present work, the kriging method is described and some of its statistical characteristics are explore...

The problem of optimal HI disturbance rejection while tracking uncertain constant or sinusoidal reference commands is considered. The internal model principle is used to ensure that the tracking error approaches zero asymptotically. Necessary conditions are given for controllers that minimize an HI disturbance rejection cost plus a worst-case integral square tracking error for transient trackin...

In this paper, a largeorder system is reduced by using the self adaptive bat algorithm (SABA) to a reduced-order approximation. The numerator coefficients of a desired reduced-order system are optimized based on integral square error minimization as an objective function pertaining to a unit-step as input. The denominator of the reduced order model is solved by stability equation method. The ef...

A new approach to polygonal approximation is presented in this paper. It starts from an initial set of dominant points (break points), where the integral square error from a given shape is zero. The proposed algorithm iteratively deletes most redundant dominant points till required approximation is achieved. Stabilization algorithm after elimination of each dominant point ensures high quality o...

This paper studies the mean and mean square convergence behaviors of the normalized least mean square (NLMS) algorithm with Gaussian inputs and additive white Gaussian noise. Using the Price’s theorem and the framework proposed by Bershad in IEEE Transactions on Acoustics, Speech, and Signal Processing (1986, 1987), new expressions for the excess mean square error, stability bound and decoupled...

in this paper, we propose and analyze an efficient matrix methodbased on bell polynomials for numerically solving nonlinear fredholm- volterraintegral equations. for this aim, first we calculate operational matrix of integration and product based on bell polynomials. by using these matrices, nonlinearfredholm-volterra integral equations reduce to the system of nonlinear algebraicequations which...

a numerical method for solving nonlinear fredholm-volterra integral equations of general type is presented. this method is based on replacement of unknown function by truncated series of well known chebyshev expansion of functions. the quadrature formulas which we use to calculate integral terms have been imated by fast fourier transform (fft). this is a grate advantage of this method which has...

In the paper, the author presents explicit and unified expressions for a sequence of improper integrals in terms of the beta functions and the Wallis ratios. Hereafter, the author derives integral representations for the Catalan numbers originating from combinatorics.