Nonhomogeneous matrix products / Darald J. Hartfiel.

Format:

Book

Author/Creator:

Hartfiel, D. J.

Language:

English

Subjects (All):

Matrices.

Physical Description:

1 online resource (ix, 224 p. ) ill.

Edition:

1st ed.

Place of Publication:

River Edge, N.J. : World Scientific, c2002.

Language Note:

English

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.

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. [217]-222) and index.

ISBN:

9786611951597

9781281951595

1281951595

9789812810052

9812810056

OCLC:

879025555