The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Alexander Garbali - One of the best experts on this subject based on the ideXlab platform.
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the domain wall partition function for the izergin korepin nineteen vertex model at a root of unity
Journal of Statistical Mechanics: Theory and Experiment, 2016Co-Authors: Alexander GarbaliAbstract:We study the domain wall partition function Z N for the ${{U}_{q}}\left(A_{2}^{(2)}\right)$ (Izergin–Korepin) integrable nineteen-vertex model on a square lattice of size N. Z N is a symmetric function of two sets of parameters: horizontal ${{\zeta}_{1}},..,{{\zeta}_{N}}$ and vertical ${{z}_{1}},..,{{z}_{N}}$ rapidities. For generic values of the parameter q we derive the Recurrence Relation for the domain wall partition function relating Z N+1 to ${{P}_{N}}{{Z}_{N}}$ , where P N is the proportionality factor in the Recurrence, which is a polynomial symmetric in two sets of variables ${{\zeta}_{1}},..,{{\zeta}_{N}}$ and ${{z}_{1}},..,{{z}_{N}}$ . After setting $q={{\text{e}}^{\text{i}\pi /3}}$ the Recurrence Relation simplifies and we solve it in terms of a Jacobi–Trudi-like determinant of polynomials generated by P N .
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the domain wall partition function for the izergin korepin 19 vertex model at a root of unity
arXiv: Mathematical Physics, 2014Co-Authors: Alexander GarbaliAbstract:We study the domain wall partition function $Z_N$ for the $U_q(A_2^{(2)})$ (Izergin-Korepin) integrable $19$-vertex model on a square lattice of size $N$. $Z_N$ is a symmetric function of two sets of parameters: horizontal $\zeta_1,..,\zeta_N$ and vertical $z_1,..,z_N$ rapidities. For generic values of the parameter $q$ we derive the Recurrence Relation for the domain wall partition function relating $Z_{N+1}$ to $P_N Z_N$, where $P_N$ is the proportionality factor in the Recurrence, which is a polynomial symmetric in two sets of variables $\zeta_1,..,\zeta_N$ and $z_1,..,z_N$. After setting $q^3=-1$ the Recurrence Relation simplifies and we solve it in terms of a Jacobi-Trudi-like determinant of polynomials generated by $P_N$.
Jan C Willems - One of the best experts on this subject based on the ideXlab platform.
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on constructing a shortest linear Recurrence Relation
IEEE Transactions on Automatic Control, 1997Co-Authors: Margreta Kuijper, Jan C WillemsAbstract:It has been shown in the literature that a formulation of the minimal partial realization problem in terms of exact modeling of a behavior lends itself to an iterative polynomial solution. For the scalar case, we explicitly present such a solution in full detail. Unlike classical solution methods based on Hankel matrices, the algorithm is constructive. It iteratively constructs a partial realization of minimal McMillian degree. The algorithm is known in information theory as the Berlekamp-Massey algorithm and is used for constructing a shortest linear Recurrence Relation for a finite sequence of numbers.
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on constructing a shortest linear Recurrence Relation
Conference on Decision and Control, 1995Co-Authors: Margreta Kuijper, Jan C WillemsAbstract:In 1968, Berlekamp and Massey presented an algorithm to compute a shortest linear Recurrence Relation for a finite sequence of numbers. It was originally designed for the purpose of decoding certain types of block codes. It later became important for cryptographic applications, namely for determining the complexity profile of a sequence of numbers. Here, the authors interpret the Berlekamp-Massey algorithm in a system-theoretic way. The authors explicitly present the algorithm as an iterative procedure to construct a behavior. The authors conclude that this procedure is the most efficient method for solving the scalar minimal partial realization problem.
Tomoyoshi Ito - One of the best experts on this subject based on the ideXlab platform.
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fast calculation of computer generated hologram using run length encoding based Recurrence Relation
Optics Express, 2015Co-Authors: Takashi Nishitsuji, Tomoyoshi Shimobaba, Takashi Kakue, Tomoyoshi ItoAbstract:Computer-Generated Holograms (CGHs) can be generated by superimposing zoneplates. A zoneplate is a grating that can concentrate an incident light into a point. Since a zoneplate has a circular symmetry, we reported an algorithm that rapidly generates a zoneplate by drawing concentric circles using computer graphic techniques. However, random memory access was required in the algorithm and resulted in degradation of the computational efficiency. In this study, we propose a fast CGH generation algorithm without random memory access using run-length encoding (RLE) based Recurrence Relation. As a result, we succeeded in improving the calculation time by 88 %, compared with that of the previous work.
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fast Recurrence Relation for computer generated hologram
Computer Physics Communications, 2012Co-Authors: Jiantong Weng, Tomoyoshi Shimobaba, Minoru Oikawa, Nobuyuki Masuda, Tomoyoshi ItoAbstract:Abstract In this paper, we derive a fast Recurrence Relation for a computer-generated-hologram (CGH). The Recurrence Relation based on Taylor expansion reduces the number of cosine computations as compared with conventional CGH formula. The Recurrence Relation calculates a CGH 7 or 8 times faster than the conventional CGH formula on a CPU and graphics processing unit (GPU). In addition, there is almost no difference between a CGH generated by the Recurrence Relation and that generated by the conventional type.
Margreta Kuijper - One of the best experts on this subject based on the ideXlab platform.
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on constructing a shortest linear Recurrence Relation
IEEE Transactions on Automatic Control, 1997Co-Authors: Margreta Kuijper, Jan C WillemsAbstract:It has been shown in the literature that a formulation of the minimal partial realization problem in terms of exact modeling of a behavior lends itself to an iterative polynomial solution. For the scalar case, we explicitly present such a solution in full detail. Unlike classical solution methods based on Hankel matrices, the algorithm is constructive. It iteratively constructs a partial realization of minimal McMillian degree. The algorithm is known in information theory as the Berlekamp-Massey algorithm and is used for constructing a shortest linear Recurrence Relation for a finite sequence of numbers.
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on constructing a shortest linear Recurrence Relation
Conference on Decision and Control, 1995Co-Authors: Margreta Kuijper, Jan C WillemsAbstract:In 1968, Berlekamp and Massey presented an algorithm to compute a shortest linear Recurrence Relation for a finite sequence of numbers. It was originally designed for the purpose of decoding certain types of block codes. It later became important for cryptographic applications, namely for determining the complexity profile of a sequence of numbers. Here, the authors interpret the Berlekamp-Massey algorithm in a system-theoretic way. The authors explicitly present the algorithm as an iterative procedure to construct a behavior. The authors conclude that this procedure is the most efficient method for solving the scalar minimal partial realization problem.
Rodica D Costin - One of the best experts on this subject based on the ideXlab platform.
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a class of matrix valued polynomials generalizing jacobi polynomials
Journal of Approximation Theory, 2009Co-Authors: Rodica D CostinAbstract:A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a three term Recurrence Relation, integral inter-Relations, and weak orthogonality Relations.
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a class of matrix valued polynomials generalizing jacobi polynomials
arXiv: Classical Analysis and ODEs, 2008Co-Authors: Rodica D CostinAbstract:A hierarchy of matrix-valued polynomials which generalize the Jacobi polynomials is found. Defined by a Rodrigues formula, they are also products of a sequence of differential operators. Each class of polynomials is complete, satisfies a two-step Recurrence Relation, integral inter-Relations, and quasi-orthogonality Relations.
