The singular value decomposition of the Gauss-Chebyshev and Lobatto-Chebyshev methods for Cauchy Singular Integral Equations
نویسندگان
چکیده
منابع مشابه
Vandermonde systems on Gauss-Lobatto Chebyshev nodes
This paper deals with Vandermonde matrices Vn whose nodes are the Gauss–Lobatto Chebyshev nodes, also called extrema Chebyshev nodes. We give an analytic factorization and explicit formula for the entries of their inverse, and explore its computational issues. We also give asymptotic estimates of the Frobenius norm of both Vn and its inverse and present an explicit formula for the determinant o...
متن کاملAn 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...
متن کاملGauss-chebyshev Quadrature Formulae for Strongly Singular Integrals
This paper presents some explicit results concerning an extension of the mechanical quadrature technique, namely, the Gauss-Jacobi numerical integration scheme, to the class of integrals whose kernels exhibit second order of singularity (i.e., one degree more singular than Cauchy). In order to ascribe numerical values to these integrals they must be understood in Hadamard's finite-part sense. T...
متن کاملDiscrete orthogonal polynomials on Gauss-Lobatto Chebyshev nodes
In this paper we present explicit formulas for discrete orthogonal polynomials over the so-called Gauss-Lobatto Chebyshev points. We also give the “three-term recurrence relation” to construct such polynomials. As a numerical application, we apply our formulas to the least-squares problem.
متن کاملA novel technique for a class of singular boundary value problems
In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1986
ISSN: 0898-1221
DOI: 10.1016/0898-1221(86)90026-x