On the Singular Cylinder Kernel

On the Volterra Integral Equation with Weakly Singular Kernel

A simple algorithm for solving the Volterra integral equation featuring a weakly singular kernel

There are many methods for numerical solutions of integral equations. In various branches of science and engineering, chemistry and biology, and physics applications integral equation is provided by many other authors. In this paper, a simple numerical method using a fuzzy, for the numerical solution of the integral equation with the weak singular kernel is provided. Finally, by providing three...

An effective method for approximating the solution of singular integral equations with Cauchy kernel type

In present paper, a numerical approach for solving Cauchy type singular integral equations is discussed. Lagrange interpolation with Gauss Legendre quadrature nodes and Taylor series expansion are utilized to reduce the computation of integral equations into some algebraic equations. Finally, five examples with exact solution are given to show efficiency and applicability of the method. Also, w...

Kernel Discriminant Analysis based on Generalized Singular Value Decomposition

In Linear Discriminant Analysis (LDA), a dimension reducing linear transformation is found in order to better distinguish clusters from each other in the reduced dimensional space. However, LDA has a limitation that one of the scatter matrices is required to be nonsingular and the nonlinearly clustered structure is not easily captured. We propose a nonlinear discriminant analysis based on kerne...

Majorization of Singular Integral Operators with Cauchy Kernel on L

Let a, b, c and d be functions in L = L(T, dθ/2π), where T denotes the unit circle. Let P denote the set of all trigonometric polynomials. Suppose the singular integral operators A and B are defined by A = aP + bQ and B = cP + dQ on P, where P is an analytic projection and Q = I − P is a co-analytic projection. In this paper, we use the Helson–Szegő type set (HS)(r) to establish the condition o...