Gaussian quadratures with respect to Discrete measures
نویسنده
چکیده
In analogy to the subject of Gaussian integration formulas we present an overview of some Gaussian summation formulas. The derivation involve polynomials that are orthogonal under discrete inner products and the resulting formulas are useful as a numerical device for summing fairly general series. Several illuminating examples are provided in order to present various aspects of this not very wellknown technique.
منابع مشابه
Quadratures for oscillatory and singular integrals
Numerical methods for strongly oscillatory and singular functions are given in this paper. Beside a summary of standard methods and product integration rules, we consider a class of complex integration methods, as well as Gaussian quadratures with respect to the oscillatory weight w(x) = xe, x ∈ [−1, 1]. Numerical examples are included.
متن کاملExact and Approximate Quadratures for Curvature Tensor Estimation
Accurate estimations of geometric properties of a surface from its discrete approximation are important for many computer graphics and geometric modeling applications. Especially, curvature estimation of a mesh is an active research area [GI04, CSM03, CP03] with many applications. The most important curvature measures on a surface are the mean curvature H, the Gaussian curvature K, and the curv...
متن کاملGaussian interval quadrature rule for exponential weights
Interval quadrature formulae of Gaussian type on R and R+ for exponential weight functions of the form w(x) = exp(−Q(x)), where Q is a continuous function on its domain and such that all algebraic polynomials are integrable with respect to w, are considered. For a given set of nonoverlapping intervals and an arbitrary n, the uniqueness of the n-point interval Gaussian rule is proved. The result...
متن کاملA Note on Tchakaloff’s Theorem
A classical result of Tchakaloff on the existence of exact quadrature formulae up to a given degree is extended to positive measures without compact support. A criterion for the existence of Gaussian quadratures for a class of such measures is also derived from the main proof.
متن کاملPresentation of K Nearest Neighbor Gaussian Interpolation and comparing it with Fuzzy Interpolation in Speech Recognition
Hidden Markov Model is a popular statisical method that is used in continious and discrete speech recognition. The probability density function of observation vectors in each state is estimated with discrete density or continious density modeling. The performance (in correct word recognition rate) of continious density is higher than discrete density HMM, but its computation complexity is very ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006