On the scalar rational interpolation problem

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August undefined, 2024

Webinterpolation points coincide, we can reformulate the scalar RIP as a scalar minimal partial realization problem. We have generalized the case where all the data are given at one point to vector data [6] and even matrix data [17]. In [18] we allowed data to be given at two points (zero and infinity). WebVector rational Bulirsch{Stoer algorithms 1925 (c) The corresponding interpolation problem in Ad(R)If the dimension of the vector space in the vector rational interpolation problem is dthen we have a corresponding interpolation problem in Ad(R): s (xi)=fi; for i= s;s+1;:::;s+ + ; where the fiare just the elements of Ad(R) corresponding to fi.The …

On the Scalar Rational Interpolation Problem - RERO DOC

WebOn the Scalar Rational Interpolation Problem - CORE Reader 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. importance of tradition and culture

On the solution of the minimal rational interpolation problem

WebLossless scalar functions: boundary interpolation, Schur algorithm and Ober’s canonical form. Martine Olivi, Bernard Hanzon, Ralf L.M. Peeters Abstract—In [1] a balanced canonical form for continuous-time lossless systems was presented. This form has a tridiagonal dynamical matrix A and the useful property that the corre- Web1 de ago. de 1990 · MINIMAL RATIONAL INTERPOLATION PROBLEM 519 (c) The elements of the first column 611, 021 and the elements of the second column 621, 622 of … 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 … importance of tractor in agriculture

Vector rational interpolation algorithms of Burlisch-Stoer-Neville …

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

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. Web18 de mar. de 2024 · In a series of fundamental papers BK Ghosh reduced the simultaneous stabilization problem to a NevanlinnaPick interpolation problem. In this paper we generalize some of these results allowing for derivative constraints. Moreover, we apply a method based on a Riccati-type matrix equation, called the Covariance Extension … importance of traffic controlsWebA new technique is derived for determining a parametrization of all minimal complexity rational functionsa(x)/b(x) interpolating an arbitrary sequence of points. Complexity … importance of traffic rules in our life

"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 … " - On the scalar rational interpolation problem

On the scalar rational interpolation problem

Model Reduction of MIMO Systems via Tangential Interpolation

WebPositive scalar curvature and exotic aspherical manifolds - Jialong DENG 邓嘉龙, YMSC Scalar curvature is interesting not only in analysis, geometry and topology but also in physics. For example, the positive mass theorem, which was proved by Schoen and Yau in 1979, is equivalent to the result that the three-dimension torus carries no Riemannian … 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: …

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Webthe scalar interpolation problem in this paper, and hence we consider C∞-behaviors B with two manifest variables (u,y) that take values in R2. A behavioral formulation of Nevanlinna-Pick interpolation has been done in [7], where a characterization of solutions of a “Subspace Nevanlinna Interpolation Problem” was obtained in terms of ... Web13 de mar. de 2024 · 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 ...

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 … 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 …

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 … 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 …

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]. …

Web1 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 … literary narrativesWebB. D. O. Anderson and A. C. Antoulas, “Rational interpolation and state variable realization”, Linear Algebra and Its Applications, Special Issue on Matrix Problems, in … literary nationalismWebAbstract. 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 … importance of traffic safety in our lifeWeb19 de jan. de 2024 · A linear problem of regression analysis is considered under the assumption of the presence of noise in the output and input variables. This approximation problem may be interpreted as an improper interpolation problem, for which it is required to correct optimally the positions of the original points in the data space so that they all lie … literary nationalism 19th centuryWebA 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,…. literary nationalism definitionWebThe core ideas are (1) representation of the rational approximant in barycentric form with interpolation at certain support points and (2) greedy selection of the support points to avoid exponential instabilities. The name AAA stands for “adaptive Antoulas--Anderson” in honor of the authors who introduced a scheme based on (1). importance of trainer in an organizationWeb5 de dez. de 1990 · DOI: 10.1109/CDC.1990.203507 Corpus ID: 122869561; The solution of the rational interpolation problem: a summary @article{Antoulas1990TheSO, … importance of training design