The rst part of this thesis concerns the formulation of numerical methods that are local in time for the solution of equations with memory. The main idea is that the solution will be updated in the Fourier domain in order to avoid evaluating time convolution integrals that have memory. This work was made possible by the development of a good quadrature[31] of the Fourier integral where a small ...

Gauss–Hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models. Unfortunately, the estimates are biased for large cluster sizes and/or intraclass correlations. We show that adaptive quadrature largely overcomes these problems. We then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependen...

We address quadrature-based approximations of the bilinear inverse form u>A−1u, where A is a real symmetric positive definite matrix, and analyze properties of the Gauss, Gauss-Radau, and Gauss-Lobatto quadrature. In particular, we establish monotonicity of the bounds given by these quadrature rules, compare the tightness of these bounds, and derive associated convergence rates. To our knowledg...

We present several new quadrature formulas in the triangle for exact integrationof polynomials. The points were computed numerically with a cardinal function algorithm whichimposes that the number of quadrature points N be equal to the dimension of a lower dimensionalpolynomial space. Quadrature forumulas are presented for up to degree d = 25, all which havepositive weights and ...

Abstract This paper studies the problem of construction of the optimal quadrature formula in the sense of Sard in (2) 2 ( 1,1) L − S.L.Sobolev space for approximate calculation of the Cauchy type singular integral. Using the discrete analogue of the operator 4 4 / d dx we obtain new optimal quadrature formulas. Furthermore, explicit formulas of the optimal coefficients are obtained. Finally, in...

We present a family of four-point quadrature rule, a generalization of Gauss-two point, Simpson’s 3/8, and Lobatto four-point quadrature rule for twice-differentiable mapping. Moreover, it is shown that the corresponding optimal quadrature formula presents better estimate in the context of four-point quadrature formulae of closed type. A unified treatment of error inequalities for different cla...

Abstract For the numerical solution of a classical two-dimensional Dirichlet exterior problem for wave equation in time domain, we consider space-time boundary integral approach, based on its discretization by means coupling discrete convolution quadrature order 2, with continuous piecewise linear element method. The latter is either Galerkin method or collocation one, this being computationall...

In [1,2,3], A. C. Baker and J.W. Baker studied the subspace Ma(S) of the convolution measure algebra M, (S) of a locally compact semigroup. H. Dzinotyiweyi in [5,7] considers an analogous measure space on a large class of C-distinguished topological semigroups containing all completely regular topological semigroups. In this paper, we extend the definitions to study the weighted semigroup ...

Quadrature transceivers utilize complex signal processing in the analog front-end (AFE) to tackle the image problem in frequency up/downconversion. The image-rejection performance is limited by the unavoidable I/Q imbalance throughout the AFE. In this paper, an in-depth analysis and modeling of I/Q mismatch effects in 3 different AFE frequency up/downconverters in SIMULINK are presented to bett...

A high-order accurate numerical quadrature algorithm is presented for the evaluation of integrals over curved surfaces and volumes which are defined implicitly via a fixed isosurface of a given function restricted to a given hyperrectangle. By converting the implicitly defined geometry into the graph of an implicitly defined height function, the approach leads to a recursive algorithm on the nu...