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Diagonal Elements (diagonal + element)
Selected AbstractsOn-line identification of non-linear hysteretic structural systems using a variable trace approachEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 9 2001Jeng-Wen Lin Abstract In this paper, an adaptive on-line parametric identification algorithm based on the variable trace approach is presented for the identification of non-linear hysteretic structures. At each time step, this recursive least-square-based algorithm upgrades the diagonal elements of the adaptation gain matrix by comparing the values of estimated parameters between two consecutive time steps. Such an approach will enforce a smooth convergence of the parameter values, a fast tracking of the parameter changes and will remain adaptive as time progresses. The effectiveness and efficiency of the proposed algorithm is shown by considering the effects of excitation amplitude, of the measurement units, of larger sampling time interval and of measurement noise. The cases of exact-, under-, over-parameterization of the structural model have been analysed. The proposed algorithm is also quite effective in identifying time-varying structural parameters to simulate cumulative damage in structural systems. Copyright © 2001 John Wiley & Sons, Ltd. [source] Gauge-independent quantum dynamics on phase-space of charged scalar particlesFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 2-3 2003S. Varró On the basis of the Hamiltonian form of the Klein-Gordon equation of a charged scalar particle field introduced by Feshbach and Villars, the gauge-invariant 2×2 Wigner matrix has been constructed whose diagonal elements describe positive and negative charge densities and the off-diagonal elements correspond to cross-densities in phase-space. The system of coupled transport equations has been derived in case of interaction with an arbitrary external electromagnetic field. A gauge-independent generalization of the free particle representation due to Feshbach and Villars is given, and on the basis of it both the nonrelativistic and the classical limits of the general relativistic quantum Boltzmann-Vlasov equation(RQBVE) is discussed. In the non-relativistic limit (p/mc,0) the set of equations of motion decouple to two independent quantum transport equations describing the dynamics of oppositely charged positon and negaton densities separately. In the classical limit(,,0) two relativistic Boltzmann-Vlasov equations result for the diagonal positon and negaton densities. It is obtained that, though in the latter equations the Planck constant , is absent, the real part of the cross-density does not vanish. [source] Multi-loop control synthesis for unstable systems and its application: An approach based on µ interaction measureINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2009Adarsha Swarnakar Abstract This paper presents a new practical framework for multi-loop controller design in which controllers are designed independently, i.e. a controller in one loop is designed without exploiting information of other controllers. The method is based on the (block) diagonal approximation of a system that is different from its (block) diagonal elements. The focus of this work is on unstable systems and the approximated systems are obtained by minimizing an upper bound of a scaled ,, norm for the error systems. This extends the applicability of conventional µ-interaction measure to a more general scenario. The proposed approach is applied to a numerical example and to a simulated industrial boiler system. Copyright © 2008 John Wiley & Sons, Ltd. [source] Systematic Study of Selected Diagonalization Methods for Configuration Interaction MatricesJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 13 2001Matthew L. Leininger Abstract Several modifications to the Davidson algorithm are systematically explored to establish their performance for an assortment of configuration interaction (CI) computations. The combination of a generalized Davidson method, a periodic two-vector subspace collapse, and a blocked Davidson approach for multiple roots is determined to retain the convergence characteristics of the full subspace method. This approach permits the efficient computation of wave functions for large-scale CI matrices by eliminating the need to ever store more than three expansion vectors (bi) and associated matrix-vector products (,i), thereby dramatically reducing the I/O requirements relative to the full subspace scheme. The minimal-storage, single-vector method of Olsen is found to be a reasonable alternative for obtaining energies of well-behaved systems to within ,Eh accuracy, although it typically requires around 50% more iterations and at times is too inefficient to yield high accuracy (ca. 10,10Eh) for very large CI problems. Several approximations to the diagonal elements of the CI Hamiltonian matrix are found to allow simple on-the-fly computation of the preconditioning matrix, to maintain the spin symmetry of the determinant-based wave function, and to preserve the convergence characteristics of the diagonalization procedure. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1574,1589, 2001 [source] Topological Electronegativity Index and Its Application , I. Ionization Potentials of Alkyl Groups and Alkyl HalidesMOLECULAR INFORMATICS, Issue 9 2007Chenzhong Cao Abstract A Topological Electronegativity Index (TEI) for alkyl group was developed, based on the bond adjacency matrix of the radical atom. Taking the radical atom and the adjacency atoms (or groups) as the vertices of molecular graph of the alkyl group, the bond adjacency matrix was constructed, in which the diagonal elements were assigned the Pauling electronegativity of the atom (or group), and the off-diagonal elements were assigned values 1 or 0. The off-diagonal elements represent the bond connections: that is when the two atoms (or groups) connect with each other, it is 1; otherwise is 0. From the matrix, the eigenvalues were obtained and its geometric mean value was considered as the TEI of an alkyl. The calculated TEI has good correlation with its experimental ionization potential. Further, the TEI was applied to correlate with the ionization potentials of alkyl halides and substituted ethenes, and to correlate with the Bond Dissociation Energies (BDEs) of the CiH bonds in alkanes. [source] Asymptotic properties of the QR factorization of banded Hessenberg,Toeplitz matricesNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 7 2005Xiao-Wen Chang Abstract We consider Givens QR factorization of banded Hessenberg,Toeplitz matrices of large order and relatively small bandwidth. We investigate the asymptotic behaviour of the R factor and Givens rotation when the order of the matrix goes to infinity, and present some interesting convergence properties. These properties can lead to savings in the computation of the exact QR factorization and give insight into the approximate QR factorizations of interest in preconditioning. The properties also reveal the relation between the limit of the main diagonal elements of R and the largest absolute root of a polynomial. Copyright © 2005 John Wiley & Sons, Ltd. [source] Maximum-weight-basis preconditionersNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 8-9 2004Erik G. Boman Abstract This paper analyses a novel method for constructing preconditioners for diagonally dominant symmetric positive-definite matrices. The method discussed here is based on a simple idea: we construct M by simply dropping offdiagonal non-zeros from A and modifying the diagonal elements to maintain a certain row-sum property. The preconditioners are extensions of Vaidya's augmented maximum-spanning-tree preconditioners. The preconditioners presented here were also mentioned by Vaidya in an unpublished manuscript, but without a complete analysis. The preconditioners that we present have only O(n+t2) nonzeros, where n is the dimension of the matrix and 1,t,n is a parameter that one can choose. Their construction is efficient and guarantees that the condition number of the preconditioned system is O(n2/t2) if the number of nonzeros per row in the matrix is bounded by a constant. We have developed an efficient algorithm to construct these preconditioners and we have implemented it. We used our implementation to solve a simple model problem; we show the combinatorial structure of the preconditioners and we present encouraging convergence results. Copyright © 2004 John Wiley & Sons, Ltd. [source] Ant colony optimization as a method for strategic genotype samplingANIMAL GENETICS, Issue 3 2009M. L. Spangler Summary A simulation study was carried out to develop an alternative method of selecting animals to be genotyped. Simulated pedigrees included 5000 animals, each assigned genotypes for a bi-allelic single nucleotide polymorphism (SNP) based on assumed allelic frequencies of 0.7/0.3 and 0.5/0.5. In addition to simulated pedigrees, two beef cattle pedigrees, one from field data and the other from a research population, were used to test selected methods using simulated genotypes. The proposed method of ant colony optimization (ACO) was evaluated based on the number of alleles correctly assigned to ungenotyped animals (AKP), the probability of assigning true alleles (AKG) and the probability of correctly assigning genotypes (APTG). The proposed animal selection method of ant colony optimization was compared to selection using the diagonal elements of the inverse of the relationship matrix (A,1). Comparisons of these two methods showed that ACO yielded an increase in AKP ranging from 4.98% to 5.16% and an increase in APTG from 1.6% to 1.8% using simulated pedigrees. Gains in field data and research pedigrees were slightly lower. These results suggest that ACO can provide a better genotyping strategy, when compared to A,1, with different pedigree sizes and structures. [source] H, control for linear systems with state saturation nonlinearities,ASIAN JOURNAL OF CONTROL, Issue 6 2009Xiaofu Ji Abstract The problem of H, control for a class of linear systems with state saturation nonlinearities is considered in this paper. By introducing a row diagonally dominant matrix with negative diagonal elements and a diagonal matrix with positive elements, the H, control problem is reduced to a matrix inequality feasibility problem that can be solved by the proposed iterative linear matrix inequality algorithm. The effectiveness of the presented method is demonstrated by a numerical example. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Asymptotic rate of quantum ergodicity in chaotic Euclidean billiardsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 10 2006Alexander Barnett The quantum unique ergodicity (QUE) conjecture of Rudnick and Sarnak is that every eigenfunction ,n of the Laplacian on a manifold with uniformly hyperbolic geodesic flow becomes equidistributed in the semiclassical limit (eigenvalue En , ,); that is, "strong scars" are absent. We study numerically the rate of equidistribution for a uniformly hyperbolic, Sinai-type, planar Euclidean billiard with Dirichlet boundary condition (the "drum problem") at unprecedented high E and statistical accuracy, via the matrix elements ,,n, Â,m, of a piecewise-constant test function A. By collecting 30,000 diagonal elements (up to level n , 7 × 105) we find that their variance decays with eigenvalue as a power 0.48 ± 0.01, close to the semiclassical estimate ½ of Feingold and Peres. This contrasts with the results of existing studies, which have been limited to En a factor 102 smaller. We find strong evidence for QUE in this system. We also compare off-diagonal variance as a function of distance from the diagonal, against Feingold-Peres (or spectral measure) at the highest accuracy (0.7%) thus far in any chaotic system. We outline the efficient scaling method and boundary integral formulae used to calculate eigenfunctions. © 2006 Wiley Periodicals, Inc. [source] | ||||||||||||||||