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Structured Matrices and Unconstrained Rational Interpolation Problems

机译：结构矩阵与无约束有理插值问题

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摘要

We describe a fast recursive algorithm for the solution of an unconstrainedrational interpolation problem by exploiting the displacement structure concept. We use the interpolation data to implicitly define a convenient non-Hermitian structured matrix, and then apply a computationally efficient procedure for its triangular factorization. This leads to a transmission-line interpretation that makes evident the interpolation properties. We further discuss connections with the Lagrange interpolating polynomial as well as questions regarding the minimality and the admissible degrees of complexity of the solutions.

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作者
Boros, T.; Sayed, A. H.; Kailath, T.;
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年度 1994
页码
总页数 35
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Interpolation; Recursive functions; Algorithms; Displacement; Problem solving; Polynomials; Lagrangian functions; Reprints;

机译：插值;递归函数;算法;位移;问题解决;多项式;拉格朗日函数;重印;

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1. Generalized confluent Cauchy-Vandermonde matrices: displacement structures, inversion formulas and tangential interpolations [J] . Zheng-Hong Yang Journal of Computational and Applied Mathematics . 2003,第2期

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2. Rational interpolation and mixed inverse spectral problem for finite CMV matrices [J] . Golinskii L., Kudryavtsev M. Journal of Approximation Theory . 2009,第1期

机译：有限CMV矩阵的有理插值和混合逆谱问题
3. J-inner matrix functions, interpolation and inverse problems for canonical systems, V: The inverse input scattering problem for Wiener class and rational pxq input scattering matrices [J] . Arov DZ, Dym H Integral equations and operator theory . 2002,第1期

机译：J-内矩阵函数，规范系统的内插和逆问题，V：维纳类和有理pxq输入散射矩阵的逆输入散射问题
4. Polynomial and rational evaluation and interpolation (with structured matrices)~* [C] . Vadim Olshevsky, Victor Y.Pan International colloquium on automata, Languages and programming . 1999

机译：多项式和合理评估和插值（具有结构矩阵）〜*
5. Effective computations with dense structured matrices and applications to polynomial evaluation and interpolation. [D] . Dias, Olen. 1997

机译：具有密集结构矩阵的有效计算及其在多项式求值和插值中的应用。
6. Penalized model-based clustering with unconstrained covariance matrices [O] . Hui Zhou, Wei Pan, Xiaotong Shen -1

机译：基于惩罚模型的无约束协方差矩阵聚类
7. Structured matrices and unconstrained rational interpolation problems [O] . Boros Tibor, Sayed Ali H., Kailath Thomas 1994

机译：结构化矩阵和无约束有理插值问题
8. Unconstrained Minimization by Interpolation: Rates of Convergence. [R] . Barzilai, J. 1981

机译：通过插值进行无约束最小化：收敛速度。

Structured Matrices and Unconstrained Rational Interpolation Problems

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