Nonhomogeneous Matrix Products.
Title:
Nonhomogeneous Matrix Products.
Author:
Hartfiel, Darald J.
ISBN:
9789812810052
Personal Author:
Physical Description:
1 online resource (236 pages)
Contents:
Contents -- Preface -- 1 Introduction -- 2 Functionals -- 2.1 Projective and Hausdorff Metrics -- 2.2 Contraction Coefficients -- 2.3 Measures of Irreducibility and Full Indecomposability -- 2.4 Spectral Radius -- 2.5 Research Notes -- 3 Semigroups of Matrices -- 3.1 Limiting Sets -- 3.2 Bounded Semigroups -- 3.3 Research Notes -- 4 Patterned Matrices -- 4.1 Scrambling Matrices -- 4.2 Sarymsakov Matrices -- 4.3 Research Notes -- 5 Ergodicity -- 5.1 Birkhoff Coefficient Results -- 5.2 Direct Results -- 5.3 Research Notes -- 6 Convergence -- 6.1 Reduced Matrices -- 6.2 Convergence to 0 -- 6.3 Results on II (Uk + Ak) -- 6.4 Joint Eigenspaces -- 6.5 Research Notes -- 7 Continuous Convergence -- 7.1 Sequence Spaces and Convergence -- 7.2 Canonical Forms -- 7.3 Coefficients and Continuous Convergence -- 7.4 Research Notes -- 8 Paracontracting -- 8.1 Convergence -- 8.2 Types of Trajectories -- 8.3 Research Notes -- 9 Set Convergence -- 9.1 Bounded Semigroups -- 9.2 Contraction Coefficient Results -- 9.3 Convexity in Convergence -- 9.4 Research Notes -- 10 Perturbations in Matrix Sets -- 10.1 Subspace Coefficient Results -- 10.2 Birkhoff Coefficient Results -- 10.3 Research Notes -- 11 Graphics -- 11.1 Maps -- 11.2 Graphing Curves -- 11.3 Graphing Fractals -- 11.4 Research Notes -- 11.5 MATLAB Codes -- 12 Slowly Varying Products -- 12.1 Convergence to 0 -- 12.2 Estimates of Xk from Current Matrices -- 12.3 State Estimates from Fluctuating Matrices -- 12.4 Quotient Spaces -- 12.5 Research Notes -- 13 Systems -- 13.1 Projective Maps -- 13.2 Demographic Problems -- 13.4 Research Notes -- 13.5 MATLAB Codes -- Appendix -- Bibliography -- Index.
Abstract:
Infinite products of matrices are used in nonhomogeneous Markov chains, Markov set-chains, demographics, probabilistic automata, production and manpower systems, tomography, and fractals. More recent results have been obtained in computer design of curves and surfaces. This book puts together much of the basic work on infinite products of matrices, providing a primary source for such work. This will eliminate the rediscovery of known results in the area, and thus save considerable time for researchers who work with infinite products of matrices. In addition, two chapters are included to show how infinite products of matrices are used in graphics and in systems work. Contents: Functionals; Semigroups of Matrices; Patterned Matrices; Ergodicity; Convergence; Continuous Convergence; Paracontracting; Set Convergence; Perturbations in Matrix Sets; Graphics; Slowly Varying Products; Systems. Readership: Researchers in applied mathematics, numerical and computational mathematics, industrial engineering, chaos and dynamical systems.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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