On the scalar rational interpolation problem

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August undefined, 2024

Web1 de jun. de 1997 · Elsevier Science Inc., 1997 INTRODUCTION The goal of this paper is to study the minimal rational interpolation problem using algebrogeometric methods. Specifically, we will deal in a unified framework with the following problems: scalar and matrix interpola- tion, and left and fight tangential interpolation. The results we will … Web28 de jun. de 1998 · The Gröbner basis approach has been applied to rational interpolation problems and to the solution of multivariable congruences [25, 26]. …

Stability and McMillan degree for rational matrix interpolants

Web1 de set. de 1988 · Furthermore, the condition 2pm. > N, guarantees uniqueness of the minimal-complexity solution. Clearly, the above condition is satisfied only in those cases for which the Euclidean algorithm is highly non-generic. REFERENCES 1 Antoulas, A. C. and Anderson, B. D. O. 1986. On the scalar rational interpolation problem, IMA 1. Math. great homes lending

A de Montessus type convergence study of a least-squares vector …

Web1 de dez. de 1992 · The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear combination of them is satisfied for each one of the N interpolation nodes. Web1 de set. de 1988 · Furthermore, the condition 2pm. > N, guarantees uniqueness of the minimal-complexity solution. Clearly, the above condition is satisfied only in those cases … WebAbstract. A new technique is derived for determining a parametrization of all minimal complexity rational functions a (x)/b (x) interpolating an arbitrary sequence of points. Complexity is measured in terms of max {deg ( a ), deg ( b) + r } where r is an arbitrary … great homes in new mexico

A new approach to the rational interpolation problem: the vector …

A general approach to multivariable recursive interpolation

WebA new formal approach to the rational interpolation problem. M. Barel, A. Bultheel. Mathematics. 1992. SummaryAn elegant and fast recursive algorithm is developed to solve the rational interpolation problem in a complementary way compared to existing methods. We allow confluent interpolation points,…. Web31 de dez. de 1990 · We generalize our earlier results on rational interpolation which were given in Van Barel and Bultheel (this journal, 1990) for the scalar case and in Bultheel and Van Barel (1990) for the vector case when all the interpolation points coincide, to the case of vector data given at arbitrary points that may coincide or not. This is the vector-valued … great homes magazineWeb1 de mar. de 1991 · The Multipoint Padé Table and General Recurrences for Rational Interpolation. ... In the case of the scalar pole-problem (also allowing confluent … floating candle centerpieces for baby shower

"WebThe fundamental scalar rational interpolation problem is to determine all interpolations (3) of the given sequence (1) and, in particular, those satisfying the minimality condition At: … " - On the scalar rational interpolation problem

On the scalar rational interpolation problem

WebA new technique is derived for determining a parametrization of all minimal complexity rational functionsa(x)/b(x) interpolating an arbitrary sequence of points. Complexity … WebIn this paper we generalize for matrix valued functions a number of well known interpolation problems for scalar rational functions and obtain explicit formulas for the solutions. The realization approach toward the study of rational matrix functions from systems theory serves here as the main tool.

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Web1 de set. de 2007 · This paper generalize for matrix valued functions a number of well known interpolation problems for scalar rational functions and obtain explicit formulas for the solutions and gives a more systematic and transparent exposition based exclusively on analysis in finite dimensional spaces. WebSummary. An elegant and fast recursive algorithm is developed to solve the rational interpolation problem in a complementary way compared to existing methods. We …

WebOur theory is in the spirit of that given by Saff [6] for the scalar rational interpolation problem and by Graves-Morris and Saff [2–4] for vector-valued rational interpolants, in particular, simultaneous Pade approximants and generalized inverse vector-valued Pad´ e approximants.´ Our proofs are completely different, however. Web1 de set. de 1986 · The rational interpolation problem in the scalar case, including multiple points, is solved. In particular a parametrization of all minimal-degree rational functions interpolating given pairs of points is derived. These considerations provide a generalization of the results on the partial realization of linear systems.

Web5 de dez. de 1990 · DOI: 10.1109/CDC.1990.203507 Corpus ID: 122869561; The solution of the rational interpolation problem: a summary @article{Antoulas1990TheSO, … Web1 de set. de 1986 · The rational interpolation problem in the scalar case, including multiple points, is solved. In particular a parametrization of all minimal-degree rational …

WebMINIMAL RATIONAL INTERPOLATION PROBLEM 515 where r:=rl+ a.0 +r,. The main result of the (left) tangential interpola- tion problem (cf. Theorem 2.11, Corollary 2.13; Theorem 3.9, Corollary 3.11; Section 4) states that the reachability indices of the above-defined pair of matrices ( Fl,G), determine the possible admissible degrees of complexity.

Webproblem of linear system theory can be interpreted as a multiple-point interpolation problem, the present approach to interpolation theory yields a novel approach to … great homes las vegasWebWe introduce a new method for Estimation of Signal Parameters based on Iterative Rational Approximation (ESPIRA) for sparse exponential sums. Our algorithm uses the AAA algorithm for rational approximation of the discr… great homes missoulaWebIn this paper, we address the problem of constructing a reduced order system of minimal McMillan degree that satisfiesa set of tangential interpolation conditions with respect to the original system under some mild conditions. The resulting reduced order transfer function appears to be generically unique and we present a simple and efficient technique to … floating candle centerpieces diyWeb1 de fev. de 2024 · Determining the constraints in the rational interpolation problem. The proposed approach solves the rational interpolation Problem 3.1 for the S 22 entry of each filter k, k = 1, …, N. The transmission zeros σ and the values v are not readily available, but can be obtained by following Proposition 3.1. Solving the rational … floating candle centerpieces bowlsWebThe matrix rational interpolation problems include the partial realization problem for matrix power series and Newton-Pade, Hermite-Pade, simulta- ... We pay particular attention to the fact that RS–xƒ‹P–xƒ=q–xƒis a scalar rational interpolant with real coe†cients. It satisﬁes the divisibility condition (iii) in Deﬁnition 2.1. floating candle centerpieces vasesWebOn the Scalar Rational Interpolation Problem - CORE Reader great homes mexicoWebThe fundamental scalar rational interpolation problem (see [1], for example) is to parametrize all rational functions y(x) = a(x) b(x) (2) interpolating these points and, … floating candle centerpieces for christmas