In this paper, a new and efficient approach is applied for numerical approximation of the linear differential equations with variable coeffcients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansion coeffcients for the moments of derivatives of any differentiable function in terms of the original expansion coefficients of the f...

We describe an algorithm for constructing point sets which admit unique Lagrange and Hermite interpolation from the space S 1 3 (() of C 1 splines of degree 3 deened on a general class of triangulations. The triangulations consist of nested polygons whose vertices are connected by line segments. In particular, we have to determine the dimension of S 1 3 (() which is not known for arbitrary tria...

A novel sparse Gauss–Hermite quadrature filter is proposed using a sparse-grid method for multidimensional numerical integration in the Bayesian estimation framework. The conventional Gauss–Hermite quadrature filter is computationally expensive for multidimensional problems, because the number of Gauss–Hermite quadrature points increases exponentially with the dimension. The number of sparse-gr...

' J. von Neumann, these PROCEEDINGS, 18, 70-82 (1932). 4E. Hopf, these PROCEEDINGS, 18, 93-100 (1932). 0G. D. Birkhoff, these PROCEEDINGS, 17, 656-660 (1931). 6 G. D. Birkhoff and P. Smith, Journal de Math., 7 [9],(1928), p. 365. 7 H. Poincar6, Calcul des Probabilitils, 2nd Edition, Paris, 1912, 320-333. 8 This remark is due to B. 0. Koopman who privately communicated it to the author two month...

| Matrix decomposition algorithms employing fast Fourier transforms were developed recently by the authors to solve the systems of linear algebraic equations that arise when piecewise Hermite bicubic orthogonal spline collocation (OSC) is applied to certain separable elliptic boundary value problems on a rectangle. In this paper, these algorithms are interpreted as Fourier methods in analogy wi...

In dynamic analysis of constrained multibody systems (MBS), the computer simulation problem essentially reduces to finding a numerical solution to higher-index differentialalgebraic equations (DAE). This paper presents a hybrid method composed of multi-input multi-output (MIMO), nonlinear, variable-structure control (VSC) theory and poststabilization from DAE solution theory for the computer so...

We show that for almost every map in a transversal one-parameter family of piecewise expanding unimodal maps the Birkhoff sum of suitable observables along the forward orbit of the turning point satisfies the law of iterated logarithm. This result will follow from an almost sure invariance principle for the Birkhoff sum, as a function on the parameter space. Furthermore, we obtain a similar res...