Gaussian quadrature for multiple orthogonal polynomials
نویسندگان
چکیده
منابع مشابه
Orthogonal Polynomials and Quadrature
Various concepts of orthogonality on the real line are reviewed that arise in connection with quadrature rules. Orthogonality relative to a positive measure and Gauss-type quadrature rules are classical. More recent types of orthogonality include orthogonality relative to a sign-variable measure, which arises in connection with Gauss-Kronrod quadrature, and power (or implicit) orthogonality enc...
متن کاملConstruction of σ-orthogonal Polynomials and Gaussian Quadrature Formulas
Let dα be a measure on R and let σ = (m1,m2, ..., mn), where mk ≥ 1, k = 1, 2, ..., n, are arbitrary real numbers. A polynomial ωn(x) := (x − x1)(x − x2)...(x − xn) with x1 ≤ x2 ≤ ... ≤ xn is said to be the n-th σ-orthogonal polynomial with respect to dα if the vector of zeros (x1, x2, ..., xn) is a solution of the extremal problem ∫
متن کاملGaussian structures and orthogonal polynomials
When asked to mention one statistical distribution, most people would probably come up with the normal distribution, also known as the Gaussian distribution after the legendary German mathematician Carl Friedrich Gauß (1777–1855). A large number of objects in life are usually considered normally distributed, for example the IQ of adult humans, the error made when measuring the mass of a protein...
متن کاملAsymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadrature
In this paper we study the asymptotic behavior of a family of polynomials which are orthogonal with respect to an exponential weight on certain contours of the complex plane. The zeros of these polynomials are the nodes for complex Gaussian quadrature of an oscillatory integral on the real axis with a high order stationary point, and their limit distribution is also analyzed. We show that the z...
متن کاملQuadrature formulas for integrals transforms generated by orthogonal polynomials
By using the three-term recurrence equation satisfied by a family of orthogonal polynomials, the Christoffel-Darboux-type bilinear generating function and their asymptotic expressions, we obtain quadrature formulas for integral transforms generated by the classical orthogonal polynomials. These integral transforms, related to the so-called Poisson integrals, correspond to a modified Fourier Tra...
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: Journal of Computational and Applied Mathematics
سال: 2005
ISSN: 0377-0427
DOI: 10.1016/j.cam.2004.04.016