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PRECONDITIONED SOR METHODS FOR GENERALIZED LEAST-SQUARES PROBLEMS

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Acta Mathematicae Applicatae Sinica 2000年第2期16卷 130-139页

作者：袁锦昀 departmento de matemática Universidade Federal do Paraná Centro Politécnico Curitiba Brazil Instituto de matemática Pura e Aplicada Rio de Janeiro Brazil

We consider here iterative methods for the generalized least squares problem defined as min(Ax-b)TW-1 (Ax-b) with W symmetric and positive definite. We develop preconditioned SOR methods specially devised also for the augmented systems of the problem. We establish the convergence region for the relaxation parameter and discuss, for one of the resulting SOR methods, the optimal value of this parameter. The convergence analysis and numerical experiments show that the preconditioned block SOR methods are very good alternatives for solving the problem.

关键词： cyclic SOR method generalized SOR method least-squares problems, generalized least-squares problems convergence optimal parameter

On a Variant of Giuga Numbers

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Acta Mathematica Sinica,English Series 2012年第4期28卷 653-660页

作者： Jos María GRAU Florian LUCA Antonio M. OLLER-MARCN departmento de matemáticas Universidad de Oviedo Avda. Calvo Sotelo s/n Instituto de matemáticas Universidad Nacional Autnoma de México The John Knopfmacher Centre for Applicable Analysis and Number Theory University of the Witwatersrand Centro Universitario de la defensa Academia General Militar Ctra. Huesca s/n

In this paper, we characterize the odd positive integers n satisfying the congruence ∑j=1^n-1 j n-1/2 We show that the set of such positive integers has an asymptotic densitywhich turns out to be slightly larger than... 详细信息

关键词： Congruence Giuga numbers asymptotic density

Relativistic versus Newtonian Frames

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Positioning 2013年第1期4卷 109-114页

作者： J.-F. Pascual-Sánchez A. San Miguel F. Vicente departmento de matemática Aplicada Facultad de Ciencias Universidad de Valladolid Valladolid Spain IMUVA and departmento de matemática Aplicada E.I.I. Universidad de Valladolid Valladolid Spain

Only a causal class among the 199 Lorentzian ones, which do not exists in the Newtonian space-time, is privileged to construct a generic, gravity free and immediate (non retarded) relativistic positioning system. This is the causal class of the null emission coordinates. Emission coordinates are defined and generated by four emitters broadcasting their proper times. The emission coordinates are covariant (frame independent) and hence valid for any user. Any observer can obtain the values of his (her) null emission coordinates from the emitters which provide him his (her) position and trajectory.

关键词： Null Emission Coordinates Location Systems Causal Class Relativistic Positioning System Gravimetry

ON THE BEST APPROXIMATION MATRIX PROBLEM FOR INTEGRABLE MATRIX FUNCTIONS

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Analysis in Theory and Applications 2000年第3期16卷 56-71页

作者： defez Emilio Jódar Lucas departmento de matemática Aplicada Umversidad Politécnica de ValenciaP.O.Box 22.012ValenciaSpain

In this paper positive definite matrix functionals defined on a set of square integrable matrix valued functions are introduced and studied. The best approximation problem is solved in terms of matrix Fourier series. ... 详细信息

关键词： ON THE BEST APPROXIMATION MATRIX PROBLEM FOR INTEGRABLE MATRIX FUNCTIONS exp Cr Lab