Quantum estimation theory

A Basic Fuzzy-Estimation Theory for Available Operation of Extremely Complicated Large-Scale Network Systems

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences ◽

10.1587/transfun.e95.a.338 ◽

2012 ◽

Vol E95-A (1) ◽

pp. 338-345 ◽

Cited By ~ 2

Author(s):

Kazuo HORIUCHI

Keyword(s):

Large Scale ◽

Estimation Theory ◽

Network Systems ◽

Large Scale Network ◽

Scale Network

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An Adaptive Combined Preconditioner with Applications in Radiation Diffusion Equations

Communications in Computational Physics ◽

10.4208/cicp.091014.060315a ◽

2015 ◽

Vol 18 (5) ◽

pp. 1313-1335 ◽

Cited By ~ 3

Author(s):

Xiaoqiang Yue ◽

Shi Shu ◽

Xiao wen Xu ◽

Zhiyang Zhou

Keyword(s):

Convergence Analysis ◽

Estimation Theory ◽

Numerical Results ◽

Diffusion Equations ◽

Condition Numbers ◽

Radiation Diffusion ◽

Discrete Problems ◽

Preconditioned Gmres

AbstractThe paper aims to develop an effective preconditioner and conduct the convergence analysis of the corresponding preconditioned GMRES for the solution of discrete problems originating from multi-group radiation diffusion equations. We firstly investigate the performances of the most widely used preconditioners (ILU(k) and AMG) and their combinations (Bco and Bco), and provide drawbacks on their feasibilities. Secondly, we reveal the underlying complementarity of ILU(k) and AMG by analyzing the features suitable for AMG using more detailed measurements on multiscale nature of matrices and the effect of ILU(k) on multiscale nature. Moreover, we present an adaptive combined preconditioner Bcoα involving an improved ILU(0) along with its convergence constraints. Numerical results demonstrate that Bcoα-GMRES holds the best robustness and efficiency. At last, we analyze the convergence of GMRES with combined preconditioning which not only provides a persuasive support for our proposed algorithms, but also updates the existing estimation theory on condition numbers of combined preconditioned systems.

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Statistical parameter estimation theory: principles and simulation studies

10.1016/bs.aiep.2021.01.002 ◽

2021 ◽

Author(s):

Annick De Backer ◽

Jarmo Fatermans ◽

Arnold J. den Dekker ◽

Sandra Van Aert

Keyword(s):

Parameter Estimation ◽

Statistical Parameter ◽

Estimation Theory ◽

Simulation Studies ◽

Statistical Parameter Estimation

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The Concentration Ellipsoid of a Random Vector Revisited

Econometric Theory ◽

10.1017/s0266466600004539 ◽

1991 ◽

Vol 7 (3) ◽

pp. 397-403 ◽

Cited By ~ 2

Author(s):

Kenneth Nordström

Keyword(s):

Quadratic Form ◽

Random Vector ◽

Crucial Role ◽

Type Inequality ◽

Estimation Theory ◽

Linear Estimation ◽

Nonnegative Definite

Alternative definitions of the concentration ellipsoid of a random vector are surveyed, and an extension of the concentration ellipsoid of Darmois is suggested as being the most convenient and natural definition. The advantage of the proposed definition in providing substantially simplified proofs of results in (linear) estimation theory is discussed, and is illustrated by new and short proofs of two key results. A not-so-well-known, but elementary, extremal representation of a nonnegative definite quadratic form, together with the corresponding Cauchy-Schwarẓ-type inequality, is seen to play a crucial role in these proofs.

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