107 research outputs found
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April l, 1988 through September 30, 1988
Structure-Preserving Model Reduction of Physical Network Systems
This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p
QUADRATURE FORMULAS FOR THE FOURIER-CHEBYSHEV COEFFICIENTS
We consider the well known Micchelli-Rivlin quadrature formula, of
highest algebraic degree of precision, for the Fourier-Chebyshev coefficients.
For analytic functions the remainder term of this quadrature formula can
be represented as a contour integral with a complex kernel. We study the
kernel, on elliptic contours with foci at the points ∓1 and a sum of semiaxes ρ > 1, for the quoted quadrature formula. Starting from the explicit
expression of the kernel, we determine the locations on the ellipses where
maximum modulus of the kernel is attained. So we derive effective L
∞-
error bounds for this quadrature formula. Complex-variable methods are
used to obtain expansions of the error in the Micchelli-Rivlin quadrature
formula over the interval [−1, 1]. Finally, effective L
1
-error bounds are also
derived for this quadrature formul
ERROR ESTIMATES OF GAUSS-TURAN QUADRATURES
A survey of our recent results on the error of Gauss-Tur´an quadrature
formulae for functions which are analytic on a neighborhood of the set of
integration is given. In particular, a computable upper bound of the error
is presented which is valid for arbitrary weight functions. A comparison is
made with the exact error and number of numerical examples, for arbitrary
weight functions, are given which show the advantages of using such rules
as well as the sharpness of the error bound. Asymptotic error estimates
when the number of nodes in the quadrature increases are presented. A
couple of numerical examples are included
- …