The Experts below are selected from a list of 2520 Experts worldwide ranked by ideXlab platform
Suresh K. Kannan - One of the best experts on this subject based on the ideXlab platform.
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Nested saturation with guaranteed Real poles
Proceedings of the 2003 American Control Conference 2003., 2024Co-Authors: Eric N. Johnson, Suresh K. KannanAbstract:The global stabilization of asymptotically null-controllable linear systems with bounded controls has been studied extensively. An early contribution was by Teel who proposed a set of nested saturators to globally asymptotically stabilize the special case of n-integrators with one input. Using this law however, the closed loop system pole locations depend on the choice of coordinate transformation used to arrive at the control law. In this paper we suggest an approach that allows the designer to pick transformations that facilitate the placement of the closed loop poles on the Negative Real Axis.
Maria Pusa - One of the best experts on this subject based on the ideXlab platform.
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solving linear systems with sparse gaussian elimination in the chebyshev rational approximation method
Nuclear Science and Engineering, 2013Co-Authors: Maria Pusa, Jaakko LeppanenAbstract:AbstractThe Chebyshev Rational Approximation Method (CRAM) has recently been introduced by the authors to solve burnup equations, and the results have been excellent. This method has been shown to be capable of simultaneously solving an entire burnup system with thousands of nuclides both accurately and efficiently. The method was prompted by an analysis of the spectral properties of burnup matrices, and it can be characterized as the best rational approximation on the Negative Real Axis. The coefficients of the rational approximation are fixed and have been reported for various approximation orders. In addition to these coefficients, implementing the method requires only a linear solver. This paper describes an efficient method for solving the linear systems associated with the CRAM approximation. The introduced direct method is based on sparse Gaussian elimination, where the sparsity pattern of the resulting upper triangular matrix is determined before the numerical elimination phase. The stability of t...
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correction to partial fraction decomposition coefficients for chebyshev rational approximation on the Negative Real Axis
arXiv: Numerical Analysis, 2012Co-Authors: Maria PusaAbstract:Chebyshev rational approximation can be a viable method to compute the exponential of matrices with eigenvalues in the vicinity of the Negative Real Axis, and it was recently applied successfully to solving nuclear fuel burnup equations. Determining the partial fraction decomposition (PFD) coefficients of this approximation can be difficult and they have been provided (for approximation orders 10 and 14) by Gallopoulos and Saad in "Efficient solution of parabolic equations by Krylov approximation methods", SIAM J. Sci. Stat. Comput., 13(1992). It was recently discovered that the order 14 coefficients contain errors and result in 100 times poorer accuracy than expected by theory. The purpose of this note is to provide the correct PFD coefficients for approximation orders 14 and 16 and to briefly discuss the approximation accuracy resulting from the erroneous coefficients.
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Rational Approximations to the Matrix Exponential in Burnup Calculations
Nuclear Science and Engineering, 2011Co-Authors: Maria PusaAbstract:The topic of this paper is solving the burnup equations using dedicated matrix exponential methods that are based on two different types of rational approximation near the Negative Real Axis. The p...
Lettington, Matthew C. - One of the best experts on this subject based on the ideXlab platform.
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Binomial polynomials mimicking Riemann's zeta function
'Informa UK Limited', 2020Co-Authors: Coffey, Mark W., Lettington, Matthew C.Abstract:The (generalised) Mellin transforms of Gegenbauer polynomials, have polynomial factors pλ n(s), whose zeros all lie on the ‘critical line’ ℜs = 1/2 (called critical polynomials). The transforms are identified in terms of combinatorial sums related to H. W. Gould’s S:4/3, S:4/2 and S:3/1 binomial coefficient forms. Their ‘critical polynomial’ factors are then identified in terms of 3F2(1) hypergeometric functions. Furthermore, we extend these results to a one-parameter family of critical polynomials that possess the functional equation pn(s;β) = ± pn (1 − s;β). Normalisation yields the rational function qλ n(s) whose denominator has singularities on the Negative Real Axis. Moreover as s → ∞ along the positive Real Axis, qλ n(s) → 1 from below. For the Chebyshev polynomials we obtain the simpler S:2/1 binomial form, and with Cn the nth Catalan number, we deduce that 4Cn−1p2n(s) and Cnp2n+1(s) yield odd integers. The results touch on analytic number theory, special function theory, and combinatorics
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Binomial Polynomials mimicking Riemann's Zeta Function
2020Co-Authors: Coffey, Mark W., Lettington, Matthew C.Abstract:The (generalised) Mellin transforms of certain Chebyshev and Gegenbauer functions based upon the Chebyshev and Gegenbauer polynomials, have polynomial factors $p_n(s)$, whose zeros lie all on the `critical line' $\Re\,s=1/2$ or on the Real Axis (called critical polynomials). The transforms are identified in terms of combinatorial sums related to H. W. Gould's S:4/3, S:4/2 and S:3/1 binomial coefficient forms. Their `critical polynomial' factors are then identified as variants of the S:4/1 form, and more compactly in terms of certain $_3F_2(1)$ hypergeometric functions. Furthermore, we extend these results to a $1$-parameter family of polynomials with zeros only on the critical line. These polynomials possess the functional equation $p_n(s;\beta)=\pm p_n(1-s;\beta)$, similar to that for the Riemann xi function. It is shown that via manipulation of the binomial factors, these `critical polynomials' can be simplified to an S:3/2 form, which after normalisation yields the rational function $q_n(s).$ The denominator of the rational form has singularities on the Negative Real Axis, and so $q_n(s)$ has the same `critical zeros' as the `critical polynomial' $p_n(s)$. Moreover as $s\rightarrow \infty$ along the positive Real Axis, $q_n(s)\rightarrow 1$ from below, mimicking $1/\zeta(s)$ on the positive Real line. In the case of the Chebyshev parameters we deduce the simpler S:2/1 binomial form, and with $\mathcal{C}_n$ the $n$th Catalan number, $s$ an integer, we show that polynomials $4\mathcal{C}_{n-1}p_{2n}(s)$ and $\mathcal{C}_{n}p_{2n+1}(s)$ yield integers with only odd prime factors. The results touch on analytic number theory, special function theory, and combinatorics.Comment: arXiv admin note: text overlap with arXiv:1306.528
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Binomial polynomials mimicking Riemann's Zeta Function
Cornell University, 2017Co-Authors: Coffey, Mark W., Lettington, Matthew C.Abstract:The (generalised) Mellin transforms of certain Chebyshev and Gegenbauer functions based upon the Chebyshev and Gegenbauer polynomials, have polynomial factors pn(s), whose zeros lie all on the `critical line' Rs=1/2 or on the Real Axis (called critical polynomials). The transforms are identified in terms of combinatorial sums related to H. W. Gould's S:4/3, S:4/2 and S:3/1 binomial coefficient forms. Their `critical polynomial' factors are then identified as variants of the S:4/1 form, and more compactly in terms of certain 3F2(1) hypergeometric functions. Furthermore, we extend these results to a 1-parameter family of polynomials with zeros only on the critical line. These polynomials possess the functional equation pn(s;β)=±pn(1−s;β), similar to that for the Riemann xi function. It is shown that via manipulation of the binomial factors, these `critical polynomials' can be simplified to an S:3/2 form, which after normalisation yields the rational function qn(s). The denominator of the rational form has singularities on the Negative Real Axis, and so qn(s) has the same `critical zeros' as the `critical polynomial' pn(s). Moreover as s→∞ along the positive Real Axis, qn(s)→1 from below, mimicking 1/ζ(s) on the positive Real line. In the case of the Chebyshev parameters we deduce the simpler S:2/1 binomial form, and with Cn the nth Catalan number, s an integer, we show that polynomials 4Cn−1p2n(s) and Cnp2n+1(s) yield integers with only odd prime factors. The results touch on analytic number theory, special function theory, and combinatorics
Eric N. Johnson - One of the best experts on this subject based on the ideXlab platform.
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Nested saturation with guaranteed Real poles
Proceedings of the 2003 American Control Conference 2003., 2024Co-Authors: Eric N. Johnson, Suresh K. KannanAbstract:The global stabilization of asymptotically null-controllable linear systems with bounded controls has been studied extensively. An early contribution was by Teel who proposed a set of nested saturators to globally asymptotically stabilize the special case of n-integrators with one input. Using this law however, the closed loop system pole locations depend on the choice of coordinate transformation used to arrive at the control law. In this paper we suggest an approach that allows the designer to pick transformations that facilitate the placement of the closed loop poles on the Negative Real Axis.
David D Ling - One of the best experts on this subject based on the ideXlab platform.
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a block rational arnoldi algorithm for multipoint passive model order reduction of multiport rlc networks
International Conference on Computer Aided Design, 1997Co-Authors: Ibrahim M Elfadel, David D LingAbstract:Work in the area of model-order reduction for RLC interconnect networks has focused on building reduced-order models that preserve the circuit-theoretic properties of the network, such as stability, passivity, and synthesizability (Silveira et al., 1996). Passivity is the one circuit-theoretic property that is vital for the successful simulation of a large circuit netlist containing reduced-order models of its interconnect networks. Non-passive reduced-order models may lead to instabilities even if they are themselves stable. We address the problem of guaranteeing the accuracy and passivity of reduced-order models of multiport RLC networks at any finite number of expansion points. The novel passivity-preserving model-order reduction scheme is a block version of the rational Arnoldi algorithm (Ruhe, 1994). The scheme reduces to that of (Odabasioglu et al., 1997) when applied to a single expansion point at zero frequency. Although the treatment of this paper is restricted to expansion points that are on the Negative Real Axis, it is shown that the resulting passive reduced-order model is superior in accuracy to the one that would result from expanding the original model around a single point. Nyquist plots are used to illustrate both the passivity and the accuracy of the reduced order models.
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a block rational arnoldi algorithm for multipoint passive model order reduction of multiport rlc networks
International Conference on Computer Aided Design, 1997Co-Authors: Ibrahim M Elfadel, David D LingAbstract:Recent work in the area of model-order reduction for RLC interconnect networks has been focused on building reduced-order models that preserve the circuit-theoretic properties of the network, such as stability, passivity, and synthesizability. Passivity is the one circuit-theoretic property that is vital for the successful simulation of a large circuit netlist containing reduced-order models of its interconnect networks. Non-passive reduced-order models may lead to instabilities even if they are themselves stable. In this paper, we address the problem of guaranteeing the accuracy and passivity of reduced-order models of multiport RLC networks at any finite number of expansion points. The novel passivity-preserving model-order reduction scheme is a block version of the rational Arnoldi algorithm. The scheme reduces to that of the PRIMA algorithm when applied to a single expansion point at zero frequency. Although the treatment of this paper is restricted to expansion points that are on the Negative Real Axis, it is shown that the resulting passive reduced-order model is superior in accuracy to the one that would result from expanding the original model around a single point. Nyquist plots are used to illustrate both the passivity and the accuracy of the reduced-order models.
