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Idempotent matrix

About: Idempotent matrix is a research topic. Over the lifetime, 540 publications have been published within this topic receiving 6717 citations.

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30 Apr 1997
TL;DR: In this article, a generalized solution of Bellman's Differential Equation and multiplicative additive asymptotics is presented, which is based on the Maslov Optimziation Theory.
Abstract: Preface. 1. Idempotent Analysis. 2. Analysis of Operators on Idempotent Semimodules. 3. Generalized Solutions of Bellman's Differential Equation. 4. Quantization of the Bellman Equation and Multiplicative Asymptotics. References. Appendix: (P. Del Moral) Maslov Optimziation Theory. Optimality versus Randomness. Index.

425 citations

Journal ArticleDOI
TL;DR: In this article, a nonlinear projection on subsemimodules is introduced, where the projection of a point is the maximal approximation from below of the point in the sub-semimmodule.

273 citations

Journal ArticleDOI
TL;DR: In this paper, an algebraic approach to idempotent functional analysis is presented, which is an abstract version of the traditional functional analysis developed by V. P. Maslov and his collaborators.
Abstract: This paper is devoted to Idempotent Functional Analysis, which is an “abstract” version of Idempotent Analysis developed by V. P. Maslov and his collaborators. We give a brief survey of the basic ideas of Idempotent Analysis. The correspondence between concepts and theorems of traditional Functional Analysis and its idempotent version is discussed in the spirit of N. Bohr's correspondence principle in quantum theory. We present an algebraic approach to Idempotent Functional Analysis. Basic notions and results are formulated in algebraic terms; the essential point is that the operation of idempotent addition can be defined for arbitrary infinite sets of summands. We study idempotent analogs of the basic principles of linear functional analysis and results on the general form of a linear functional and scalar products in idempotent spaces.

222 citations

Journal ArticleDOI
TL;DR: In this article, an estimator design problem is considered which involves both L 2 (least squares) and H ∞ (worst-case frequency-domain) aspects, and the goal of the problem is to minimize an L 2 state-estimation error criterion subject to a prespecified h ∞ constraint on the state estimation error.

212 citations

07 May 2001
TL;DR: In this paper, the Laplace-Fenchel model is used to transform Idempotent Probability Measures on topological spaces into Projective Limits and Maxingales Stopping Times.
Abstract: IDEMPOTENT PROBABILITY THEORY Idempotent Probability Measures Idempotent Measures Measurable Maps Modes of Convergence Idempotent Integration Product Spaces Independence and Conditioning Idempotent Distributions and Laplace-Fenchel Transforms' Idempotent Measures on Topological Spaces Idemptent Measures on Projective Limits Topological Spaces of Idempotent Probabilities Maxingales Stopping Times Idempotent Stochastic Processes Exponential Maxingales Wiener and Poisson Idempotent Processes Continuous Local Maxingales Idempotent Ito Equations Semimaxingales and Maxingale Problems Proofs of the Uniqueness Results Convergence of Idempotent Processes LARGE DEVIATION CONVERGENCE Large Deviation Convergence in Tihonov Spaces General Theory Large Deviation Convergence in the Skorohod Space The Method of Finite-Dimensional Distributions Convergence of Stochastic Exponentials LD Convergence via Convergence of the Characteristics Corollaries The Method of the Maxingale Problem Convergence of Stochastic Exponentials Convergence of Characteristics APPLICATIONS Markov Processes Queueing Networks APPENDIX

143 citations

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