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Chung-kwan Chu - One of the best experts on this subject based on the ideXlab platform.
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a fast passivity test for stable descriptor systems via skew Hamiltonian Hamiltonian Matrix pencil transformations
IEEE Transactions on Circuits and Systems, 2008Co-Authors: Ngai Wong, Chung-kwan ChuAbstract:Passivity of a linear system is an important property to guarantee stable global simulation. Most circuits and interconnected systems are naturally described as descriptor systems (DSs) or singular state spaces. Passivity tests for DSs, however, are much less developed compared to their regular (nonsingular) state space counterparts. For large-scale DSs, the existing linear-Matrix-inequality test is computationally prohibitive. Other system decoupling techniques involve complicated algorithms and sometimes ill-conditioned transformations. This paper proposes a simple DS passivity test based on the insight that the sum of a passive system and its adjoint must render an impulse-free system under minimal realization. The proper part (nonimpulsive part) and the residue Matrix at infinity (impulsive part), if any, of a passive DS are conveniently extracted using numerically efficient skew-Hamiltonian/Hamiltonian Matrix pencil techniques. Numerical experiments confirm the effectiveness of the proposed test over conventional approaches.
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A Fast Passivity Test for Stable Descriptor Systems via Skew-Hamiltonian/Hamiltonian Matrix Pencil Transformations
IEEE Transactions on Circuits and Systems I: Regular Papers, 2008Co-Authors: Ngai Wong, Chung-kwan ChuAbstract:Passivity of a linear system is an important property to guarantee stable global simulation. Most circuits and interconnected systems are naturally described as descriptor systems (DSs) or singular state spaces. Passivity tests for DSs, however, are much less developed compared to their regular (nonsingular) state space counterparts. For large-scale DSs, the existing linear-Matrix-inequality test is computationally prohibitive. Other system decoupling techniques involve complicated algorithms and sometimes ill-conditioned transformations. This paper proposes a simple DS passivity test based on the insight that the sum of a passive system and its adjoint must render an impulse-free system under minimal realization. The proper part (nonimpulsive part) and the residue Matrix at infinity (impulsive part), if any, of a passive DS are conveniently extracted using numerically efficient skew-Hamiltonian/Hamiltonian Matrix pencil techniques. Numerical experiments confirm the effectiveness of the proposed test over conventional approaches.
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Transformations of Skew-Hamiltonian/Hamiltonian Matrix Pencils
2006Co-Authors: Ngai Wong, Chung-kwan ChuAbstract:ityl orpositive realness inaVLSImodel isanimportant property Passivity inaVLSImodel isanimportant property toguarantee sta- toguarantee stable global simulation [3,7]. Existing DSpassivity bleglobal simulation. MostVLSImodels arenaturally describedtests arerestrnctive indifferent aspects. Forexample, theextended asdescriptor systems (DSs) orsingular state spaces. Passivity tests linear Matrix inequality (LMI) testin[7] hasahigh complexity forDSs,however, aremuchless developed compared totheir non- of0(n5) to0(n6), rendering itprohibitive intesting passivity of singular state space counterparts. Forlarge-scale DSs,theexistinghigh-order DSs,asisusual forVLSImodels. Thegeneralized altest based onlinear Matrix inequality (LMI) iscomputationally pro- gebraic Riccati equation (GARE) test [8]worksonlyinthelimited hibitive. Other system decoupling techniques involve complicatedcaseofadmissible (regular, stable andimpulse-free) DSs. coding andsometimes ill-conditioned transformations. This paper Thecontribution ofthis paper istheformulation ofafast0(n3) proposes asimple DSpassivity test based onthekeyinsight that algorithm forchecking passivity ofaDS.Thekeyinsight isthat thesumofapassive system andits adjoint mustbeimpulse-free. whena(possibly impulsive) passive system isadded toits adjoint, A sidetrack showsthat theproper (non-impulsive) partofapas- theresulting system, whichisagain aDS,mustbeimpulse-free. sive DScanbeeasily decoupled along thetest flow. NumericalNumerically efficient andreliable techniques intransforming skewexamples confirm theeffectiveness oftheproposed DSpassivity Hamiltonian/Hamiltonian (SHH) Matrix pencils areemployed. Aftest overconventional approaches. terremoval ofuncontrollable andunobservable impulsive modes, ifany, passivity canthen bechecked through thepositive semidefinite oftheresidue Matrix andtheproper part oftheDSusing stanCategories andSubject Descriptors
Ron Shepard - One of the best experts on this subject based on the ideXlab platform.
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Evaluation of the spin-orbit interaction within the graphically contracted function method.
The journal of physical chemistry. A, 2009Co-Authors: Scott R. Brozell, Ron ShepardAbstract:The graphically contracted function (GCF) method is extended to include an effective one-electron spin-orbit (SO) operator in the Hamiltonian Matrix construction. Our initial implementation is based on a multiheaded Shavitt graph approach that allows for the efficient simultaneous computation of entire blocks of Hamiltonian Matrix elements. Two algorithms are implemented. The SO-GCF method expands the spin-orbit wave function in the basis of GCFs and results in a Hamiltonian Matrix of dimension N{sub dim} = N{sub a} ((S{sub max} + 1){sup 2} ? S{sub min}{sup 2}). N{sub a} is the number of sets of nonlinear arc factor parameters, and S{sub min} and S{sub max} are respectively the minimum and maximum values of an allowed spin range in the wave function expansion. The SO-SCGCF (SO spin contracted GCF) method expands the wave function in a basis of spin contracted functions and results in a Hamiltonian Matrix of dimension N{sub dim} = N{sub a}. For a given N{sub a} and spin range, the number of parameters defining the wave function is the same in the two methods after accounting for normalization. The full Hamiltonian Matrix construction with both approaches scales formally as O(N{sub a}{sup 2}{omega}n{sup 4}) for n molecular orbitals. The {omega} factormore » depends on the complexity of the Shavitt graph and includes factors such as the number of electrons, N, and the number of interacting spin states. Timings are given for Hamiltonian Matrix construction for both algorithms for a range of wave functions with up to N = n = 128 and that correspond to an underlying linear full-CI CSF expansion dimension of over 10{sup 75} CSFs, many orders of magnitude larger than can be considered using traditional CSF-based spin-orbit CI approaches. For Hamiltonian Matrix construction, the SO-SCGCF method is slightly faster than the SO-GCF method for a given N{sub a} and spin range. The SO-GCF method may be more suitable for describing multiple states, whereas the SO-SCGCF method may be more suitable for describing single states.« less
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Hamiltonian Matrix and reduced density Matrix construction with nonlinear wave functions.
The journal of physical chemistry. A, 2006Co-Authors: Ron ShepardAbstract:An efficient procedure to compute Hamiltonian Matrix elements and reduced one- and two-particle density matrices for electronic wave functions using a new graphical-based nonlinear expansion form is presented. This method is based on spin eigenfunctions using the graphical unitary group approach (GUGA), and the wave function is expanded in a basis of product functions (each of which is equivalent to some linear combination of all of the configuration state functions), allowing application to closed- and open-shell systems and to ground and excited electronic states. In general, the effort required to construct an individual Hamiltonian Matrix element between two product basis functions HMN = 〈M|Ĥ|N〉 scales as 𝒪 (βn4) for a wave function expanded in n molecular orbitals. The prefactor β itself scales between N0 and N2, for N electrons, depending on the complexity of the underlying Shavitt graph. Timings with our initial implementation of this method are very promising. Wave function expansions that are ord...
Ngai Wong - One of the best experts on this subject based on the ideXlab platform.
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a fast passivity test for stable descriptor systems via skew Hamiltonian Hamiltonian Matrix pencil transformations
IEEE Transactions on Circuits and Systems, 2008Co-Authors: Ngai Wong, Chung-kwan ChuAbstract:Passivity of a linear system is an important property to guarantee stable global simulation. Most circuits and interconnected systems are naturally described as descriptor systems (DSs) or singular state spaces. Passivity tests for DSs, however, are much less developed compared to their regular (nonsingular) state space counterparts. For large-scale DSs, the existing linear-Matrix-inequality test is computationally prohibitive. Other system decoupling techniques involve complicated algorithms and sometimes ill-conditioned transformations. This paper proposes a simple DS passivity test based on the insight that the sum of a passive system and its adjoint must render an impulse-free system under minimal realization. The proper part (nonimpulsive part) and the residue Matrix at infinity (impulsive part), if any, of a passive DS are conveniently extracted using numerically efficient skew-Hamiltonian/Hamiltonian Matrix pencil techniques. Numerical experiments confirm the effectiveness of the proposed test over conventional approaches.
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A Fast Passivity Test for Stable Descriptor Systems via Skew-Hamiltonian/Hamiltonian Matrix Pencil Transformations
IEEE Transactions on Circuits and Systems I: Regular Papers, 2008Co-Authors: Ngai Wong, Chung-kwan ChuAbstract:Passivity of a linear system is an important property to guarantee stable global simulation. Most circuits and interconnected systems are naturally described as descriptor systems (DSs) or singular state spaces. Passivity tests for DSs, however, are much less developed compared to their regular (nonsingular) state space counterparts. For large-scale DSs, the existing linear-Matrix-inequality test is computationally prohibitive. Other system decoupling techniques involve complicated algorithms and sometimes ill-conditioned transformations. This paper proposes a simple DS passivity test based on the insight that the sum of a passive system and its adjoint must render an impulse-free system under minimal realization. The proper part (nonimpulsive part) and the residue Matrix at infinity (impulsive part), if any, of a passive DS are conveniently extracted using numerically efficient skew-Hamiltonian/Hamiltonian Matrix pencil techniques. Numerical experiments confirm the effectiveness of the proposed test over conventional approaches.
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Transformations of Skew-Hamiltonian/Hamiltonian Matrix Pencils
2006Co-Authors: Ngai Wong, Chung-kwan ChuAbstract:ityl orpositive realness inaVLSImodel isanimportant property Passivity inaVLSImodel isanimportant property toguarantee sta- toguarantee stable global simulation [3,7]. Existing DSpassivity bleglobal simulation. MostVLSImodels arenaturally describedtests arerestrnctive indifferent aspects. Forexample, theextended asdescriptor systems (DSs) orsingular state spaces. Passivity tests linear Matrix inequality (LMI) testin[7] hasahigh complexity forDSs,however, aremuchless developed compared totheir non- of0(n5) to0(n6), rendering itprohibitive intesting passivity of singular state space counterparts. Forlarge-scale DSs,theexistinghigh-order DSs,asisusual forVLSImodels. Thegeneralized altest based onlinear Matrix inequality (LMI) iscomputationally pro- gebraic Riccati equation (GARE) test [8]worksonlyinthelimited hibitive. Other system decoupling techniques involve complicatedcaseofadmissible (regular, stable andimpulse-free) DSs. coding andsometimes ill-conditioned transformations. This paper Thecontribution ofthis paper istheformulation ofafast0(n3) proposes asimple DSpassivity test based onthekeyinsight that algorithm forchecking passivity ofaDS.Thekeyinsight isthat thesumofapassive system andits adjoint mustbeimpulse-free. whena(possibly impulsive) passive system isadded toits adjoint, A sidetrack showsthat theproper (non-impulsive) partofapas- theresulting system, whichisagain aDS,mustbeimpulse-free. sive DScanbeeasily decoupled along thetest flow. NumericalNumerically efficient andreliable techniques intransforming skewexamples confirm theeffectiveness oftheproposed DSpassivity Hamiltonian/Hamiltonian (SHH) Matrix pencils areemployed. Aftest overconventional approaches. terremoval ofuncontrollable andunobservable impulsive modes, ifany, passivity canthen bechecked through thepositive semidefinite oftheresidue Matrix andtheproper part oftheDSusing stanCategories andSubject Descriptors
Ding Ke-wei - One of the best experts on this subject based on the ideXlab platform.
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Symplectic algorithm for testing the Hamiltonian Matrix
Journal of Hefei University of Technology, 2006Co-Authors: Ding Ke-weiAbstract:The symplectic algorithm for testing Hamiltonian Matrix structure is established in the process of reducing the Hamiltonian Matrix.The resulting method works with symplectic similarity transformation which reflects the structure of the Hamiltonian matrices.This algorithm is simple and feasible and has preferable validity and stability.
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The symplectic algorithm method for forming Hamiltonian Matrix eigenpairs problem
Journal of Anhui Institute of Architecture, 2005Co-Authors: Ding Ke-weiAbstract:Hamilton canonical equation is widely studied in dynamical astronomy and cybernetics. The symplectic algorithm method for forming Hamiltonian Matrix structure is established in process of reducing of Hamiltonian Matrix. This method works with symplectic similarity transformation which reflects the structure of the Hamiltonian matrices. This algorithm can be found simpleness and feasible, and has preferable validity and stability
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The Symplectic Algorithm Method for Solving Hamiltonian Matrix by Means of Reduction of Squared
Journal of Anhui University of Science and Technology, 2005Co-Authors: Ding Ke-weiAbstract:The solution has been rather attractive for long to Algebra eigenvalue problem of Hamiltonian Matrix since it shows the difference adequately between the classical mathematics and the numerical analysis. It seems that it is very simply to solve eigenvalue problem because its basic principles are familiar to scientists. However, the challenging problem will occur in process of solving its exact solution. the symplectic algorithm method is established to solve Hamiltonian Matrix eigenvalue, which is widely studied in dynamical astronomy and cybernetics. In the course of reducing of Hamiltonian Matrix, this method works with symplectic similarity transformation applied, and keeps well the structure of the Hamiltonian matrices. This algorithm finds simpleness and feasibility, and has preferable validity and stability.
Robert J Buenker - One of the best experts on this subject based on the ideXlab platform.
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Hamiltonian Matrix representations for the determination of approximate wave functions for molecular resonances
2018Co-Authors: Robert J BuenkerAbstract:Wave functions obtained using a standard complex Hamiltonian Matrix diagonalization procedure are square integrable and therefore constitute only approximations to the corresponding resonance solutions of the Schrodinger equation. The nature of this approximation is investigated by means of explicit calculations using the above method which employ accurate diabatic potentials of the B 1 Σ + - D’ 1 Σ + vibronic resonance states of the CO molecule. It is shown that expanding the basis of complex harmonic oscillator functions gradually improves the description of the exact resonance wave functions out to ever larger internuclear distances before they take on their unwanted bound-state characteristics. The justification of the above Matrix method has been based on a theorem that states that the eigenvalues of a complex-scaled Hamiltonian H (Re iΘ ) are associated with the energy position and linewidth of resonance states (R is an internuclear coordinate and Θ is a real number). It is well known, however, that the results of the approximate method can be obtained directly using the unscaled Hamiltonian H (R) in real coordinates provided a particular rule is followed for the evaluation of the corresponding Matrix elements. It is shown that the latter rule can itself be justified by carrying out the complex diagonalization of the Hamiltonian in real space via a product of two transformation matrices, one of which is unitary and the other is complex orthogonal, in which case only the symmetric scalar product is actually used in the evaluation of all Matrix elements. There is no limit on the accuracy of the above Matrix method with an unrotated Hamiltonian, so that exact solutions of the corresponding Schrodinger equation can in principle be obtained with it. This procedure therefore makes it unnecessary to employ a complex-scaled Hamiltonian to describe resonances and eliminates any advantages that have heretofore been claimed for its use.
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a new table direct configuration interaction method for the evaluation of Hamiltonian Matrix elements in a basis of linear combinations of spin adapted functions
Journal of Chemical Physics, 1995Co-Authors: Stefan Krebs, Robert J BuenkerAbstract:A new table‐direct CI (TDCI) scheme based on the table CI method for the direct computation of Hamiltonian Matrix elements whose basis functions are linear combinations of spin‐adapted functions ψα is presented, in which the explicit calculation and storage of the Hamiltonian Matrix H in the basis {ψα} is avoided. Two algorithms are provided for the Matrix element evaluation; (i) within the iterative Davidson diagonalization procedure of H and (ii) within the individualized configuration selection scheme of Buenker and Peyerimhoff, as included in the MRD‐CI program of these authors. The new algorithm is employed to compute the equilibrium structural parameters of the lowest X 2A1 and A 2B2 states of NO2, solving secular equations of dimension 190 000 spin‐adapted functions (384 000 determinants, 32 000 configurations), as well as the Te value for the corresponding transition.
