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New Convergence Results for DavidsonType algorithms
"... In this paper we present a proof of convergence for a preconditioned subspace method (the Generalized Davidson Algorithm) which shows the dependency of the convergence rate on the preconditioner used. This convergence rate depends only on the condition of the preconditioned system 2 (MA) and th ..."
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and Sadkane [3]. However, they do not obtain any estimates of the rate of convergence, or explain its dependence on the preconditioner chosen. More specific results, including results relating the preconditioner with convergence results were developed by Oliveira [6, 7]. Let A be the given matrix whose
New convergence results on the global GMRES method for diagonalizable matrices
"... In the present paper, we give some new convergence results of the global GMRES method for multiple linear systems. In the case where the coefficient matrix A is diagonalizable, we derive new upper bounds for the Frobenius norm of the residual. We also consider the case of normal matrices and we prop ..."
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In the present paper, we give some new convergence results of the global GMRES method for multiple linear systems. In the case where the coefficient matrix A is diagonalizable, we derive new upper bounds for the Frobenius norm of the residual. We also consider the case of normal matrices and we
HOMOGENIZATION AND TWOSCALE CONVERGENCE
, 1992
"... Following an idea of G. Nguetseng, the author defines a notion of "twoscale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in L2(f) are proven to be relatively compact with respect to this new type of convergence. A corrector ..."
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Cited by 451 (14 self)
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Following an idea of G. Nguetseng, the author defines a notion of "twoscale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in L2(f) are proven to be relatively compact with respect to this new type of convergence. A corrector
SOME NEW CONVERGENCE RESULTS AND APPLICATIONS OF A CLASS OF INTERPOLATINGDERIVATIVE SPLINES
"... Abstract. In this paper we construct quadrature rules for the numerical evaluation of some singular integrals by using the interpolatingderivative splines. Convergence properties and numerical results are given. 1. ..."
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Abstract. In this paper we construct quadrature rules for the numerical evaluation of some singular integrals by using the interpolatingderivative splines. Convergence properties and numerical results are given. 1.
A NEW CONVERGENCE RESULT FOR THE RICCI FLOW IN HIGHER DIMENSIONS
, 706
"... In a previous paper, the first author and Richard Schoen proved the following theorem, which implies the differentiable sphere theorem: Theorem 1 ([2], Theorem 3). Let (M,g0) be a compact manifold of dimension n ≥ 4. Assume that the curvature tensor of g0 satisfies R(ϕ,ϕ) + ..."
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Cited by 1 (0 self)
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In a previous paper, the first author and Richard Schoen proved the following theorem, which implies the differentiable sphere theorem: Theorem 1 ([2], Theorem 3). Let (M,g0) be a compact manifold of dimension n ≥ 4. Assume that the curvature tensor of g0 satisfies R(ϕ,ϕ) +
Reopening the Convergence Debate: A new look at crosscountry growth empirics
 JOURNAL OF ECONOMIC GROWTH
, 1996
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SelfSimilarity Through HighVariability: Statistical Analysis of Ethernet LAN Traffic at the Source Level
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1997
"... A number of recent empirical studies of traffic measurements from a variety of working packet networks have convincingly demonstrated that actual network traffic is selfsimilar or longrange dependent in nature (i.e., bursty over a wide range of time scales)  in sharp contrast to commonly made tr ..."
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Cited by 743 (24 self)
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traffic modeling assumptions. In this paper, we provide a plausible physical explanation for the occurrence of selfsimilarity in LAN traffic. Our explanation is based on new convergence results for processes that exhibit high variability (i.e., infinite variance) and is supported by detailed statistical
New results in linear filtering and prediction theory
 TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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Cited by 607 (0 self)
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statistics. The variance equation is closely related to the Hamiltonian (canonical) differential equations of the calculus of variations. Analytic solutions are available in some cases. The significance of the variance equation is illustrated by examples which duplicate, simplify, or extend earlier results
Convergence Properties of the NelderMead Simplex Method in Low Dimensions
 SIAM Journal of Optimization
, 1998
"... Abstract. The Nelder–Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder–Mead algorithm. This paper pr ..."
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Cited by 598 (3 self)
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presents convergence properties of the Nelder–Mead algorithm applied to strictly convex functions in dimensions 1 and 2. We prove convergence to a minimizer for dimension 1, and various limited convergence results for dimension 2. A counterexample of McKinnon gives a family of strictly convex functions
The particel swarm: Explosion, stability, and convergence in a multidimensional complex space
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTION
"... The particle swarm is an algorithm for finding optimal regions of complex search spaces through interaction of individuals in a population of particles. Though the algorithm, which is based on a metaphor of social interaction, has been shown to perform well, researchers have not adequately explained ..."
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Cited by 852 (10 self)
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’s convergence tendencies. Some results of the particle swarm optimizer, implementing modifications derived from the analysis, suggest methods for altering the original algorithm in ways that eliminate problems and increase the optimization power of the particle swarm
Results 1  10
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