We address the problem of computing IMSE-optimal designs for random field interpolation models. A spectral representation of the IMSE criterion is obtained from the eigendecomposition of the integral operator defined by the covariance kernel of the random field and integration measure considered. The IMSE can then be approximated by spectral truncation and bounds on the error induced by this tr...

Generalized averaged Gaussian quadrature formulas may yield higher accuracy than Gauss quadrature formulas that use the same moment information. This makes them attractive to use when moments or modified moments are cumbersome to evaluate. However, generalized averaged Gaussian quadrature formulas may have nodes outside the convex hull of the support of the measure defining the associated Gauss...

The primary goal of this work is to solve the problem drug diffusion through a thin membrane using differential quadrature approach with drastically different shape functions, such as Lagrange interpolation and discrete singular convolution (the delta kernel regularized Shannon kernel). A nonlinear partial equation two time- space-dependent variables governs system. To reduce independent by one...

We consider certain quadrature rules of highest algebraic degree of precision that involve strong Stieltjes distributions (i.e., strong distributions on the positive real axis). The behavior of the parameters of these quadrature rules, when the distributions are strong c-inversive Stieltjes distributions, is given. A quadrature rule whose parameters have explicit expressions for their determina...

A positive quadrature formula with n nodes which is exact for polynomials of degree In — r — 1, 0 < r < « , is based on the zeros of certain quasi-orthogonal polynomials of degree n . We show that the quasi-orthogonal polynomials that lead to the positive quadrature formulae can all be expressed as characteristic polynomials of a symmetric tridiagonal matrix with positive subdiagonal entries. A...

This paper focuses on an optimal quadrature error correction method for the dual-mass MEMS gyroscope, in order to reduce the long term bias drift. It is known that the coupling stiffness and demodulation error are important elements causing bias drift. The coupling stiffness in dual-mass structures is analyzed. The experiment proves that the left and right masses' quadrature errors are differen...

Recursive inverse filtering with non-stationary filters is becoming a useful tool in a range of applications, from multi-dimensional inverse problems to wave extrapolation. I formulate causal non-stationary convolution and combination and their adjoints in such a way that it is apparent that the corresponding non-stationary recursive filters are true inverse processes. Stationary recursive inve...

in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...

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...