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Fast Algorithms for Solving Toeplitz System of Equations and Finding Rational Hermite Interpolants

机译：求解Toeplitz方程组并求出有理Hermite插值的快速算法

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We present a new algorithm that reduces the computation for solving a Toeplitz system to o(n log2 n) and automatically resolves all degenerate cases of the past. Our fundamental results show that all rational Hermite interpolants, including Pade approximants which is intimately related to this solution process, can be computed fast by an Euclidean algorithm. In this report we bring out all these relationship with mathematical justifications and mention important applications including decoding BCH codes. (Author)

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作者
Yun, D. Y. Y.;
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年度 1979
页码 p.1-12
总页数 12
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Interpolation; Linear algebra; Algorithms; Sequences(Mathematics); Polynomials; Solutions(General); Matrix theory; Decoding;

机译：插值;线性代数;算法;序列（数学）;多项式;解（通用）;矩阵理论;解码;

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专利

1. Matrices of small Toeplitz rank, certain representations of the solution to an unstable system of linear equations with Toeplitz coefficient matrices, and related fast algorithms for solving such systems [J] . Gelfgat V. I. Computational mathematics and mathematical physics . 2014,第11期

机译：Toeplitz等级小的矩阵，具有Toeplitz系数矩阵的线性方程组不稳定系统解的某些表示形式以及解决此类系统的相关快速算法
2. Levinson-like and Schur-like fast algorithms for solving block-slanted Toeplitz systems of equations arising in wavelet-based solution of integral equations [J] . Joshi R.R., Yagle A.E. IEEE Transactions on Signal Processing . 1998,第7期

机译：求解类似于小波的积分方程组中出现的块倾斜Toeplitz方程组的类Levinson和Schur类快速算法
3. Split versions of the Levinson-like and Schur-like fast algorithms for solving block-slanted-Toeplitz systems of equations [J] . Joshi R.R., Yagle A.E. IEEE Transactions on Signal Processing . 1998,第7期

机译：类似于Levinson和Schur的快速算法的分离版本，用于求解方程组的块倾斜Toeplitz系统
4. A Levinson-like fast algorithm for solving block-slanted Toeplitz systems of equations arising in wavelet-based solution of integral equations [C] . Joshi, R.R., Yagle, . 1996

机译：一种基于Levinson的快速算法，用于求解基于小波的积分方程组引起的方程的块倾斜Toeplitz方程组
5. High-performance algorithms to solve Toeplitz and block Toeplitz matrices [D] . Thirumalai, Srikanth 1996

机译：用于解决Toeplitz和块Toeplitz矩阵的高性能算法
6. Multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth Banach spaces with applications [O] . Yongchun Xu, Jinyu Guan, Yanxia Tang, -1

机译：非膨胀算子方程的多元系统及其在一致凸和一致光滑Banach空间中求解它们的迭代算法及其应用
7. Application of the Parallel Dichotomy Algorithm for solving Toeplitz tridiagonal systems of linear equations with one right-hand side [O] . Terekhov, Andrew V. 2015

机译：并行二分法算法在Toeplitz中的应用具有一个右侧的三对角线性方程组

Fast Algorithms for Solving Toeplitz System of Equations and Finding Rational Hermite Interpolants

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