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In the field of system modeling, circuit synthesis and filter design, it is very important to approximate a given characteristic function by a rational function of an appropriate order. Padé approximation has been known for a long time and is one of the rational function approximation methods used extensively because of its simplicity. This paper proposes to investigate N-point Padé approximation, from the system-theoretic viewpoint. The N-point Padé approximation is a rational function interpolation including the derivative of arbitrary order and, compared to regular Padé approximation and rational Hermite interpolation. In this paper we discuss the following subjects on rational function approximation of given characteristic function: its explicit form, minimal order realization problem, Nuttall's compact form, its relation to continued fractions, and the numerical efficient iterative algorithm. These are more general discussions, even including regular Padé approximation. Also, we give numerical results of the approximation of a transfer function for continuous and discrete systems as an example of application of N-point Padé approximation. [ABSTRACT FROM AUTHOR]

The translation matrix for the multilevel fast multipole algorithm (MLFMA) in an FISC (fast Illinois solver code) is calculated directly, and the complexity is O(N3/2), where N is the number of unknowns. For a problem with a small electrical size, the CPU time for calculating the translation matrix can be negligible. But for large problems, the calculation time increases significantly. In this paper, we use interpolation to calculate the translation matrix, and the complexity is reduced to O(N). Different interpolation techniques are tested, and it is found that the Lagrange polynomial interpolation with high sampling rates is the best. The saving factor is 10 for the VFY218 at 4 GHz. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 30: 109–114, 2001. [ABSTRACT FROM AUTHOR]

Given convex scattered data in R3 we consider the constrained interpolation problem of finding a smooth, minimal Lp-norm (1 < p < ∞) interpolation network that is convex along the edges of an associated triangulation. In previous work the problem has been reduced to the solution of a nonlinear system of equations. In this paper we formulate and analyse a Newton-type algorithm for solving the corresponding type of systems. The correctness of the application of the proposed method is proved and its superlinear (in some cases quadratic) convergence is shown. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]