Screen LibraryNonhomogeneous matrix products /
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 o...
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| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore : |
| Publication Dates: | 2002. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/4707#t=toc |
| Summary: |
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. |
| Carrier Form: | 1 online resource (ix,224pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages [217]-222) and index. |
| ISBN: | 9789812810052 |
| Index Number: | QA188 |
| CLC: | O151.21 |
| Contents: | 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. 13.3. Business, man power, production systems. 13.4. Research notes. 13.5. MATLAB codes. |