Overview

This second edition brings the reader on par with the flurry of research results generated during the last two decades in the theory and applications of multidimensional systems. The book has many examples to illustrate advanced concepts and presents algorithms for bivariate polynomial matrix factorization results that form the basis of two-dimensional systems theory. The reader is alerted to the reasons for the difficulties in generalization to the higher dimensional case. Algorithms and their implementation using symbolic algebra are emphasized.

Full Product Details

Author:   N.K. Bose
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2nd ed. 1995
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   1.290kg
ISBN:  

9781402016233

ISBN 10:   1402016239
Pages:   269
Publication Date:   30 November 2003
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

List of Acronyms. List of Notations. Preface. Acknowledgements. Introduction. 1: Trends in Multidimensional Systems Theory. 1. Introduction. 2. Multidimensional Systems Stability. 3. Multivariate Realization Theory. 4. n-D Problem of Moments and its Applications in Multidimensional Systems Theory. 5. Role of Irreducible Polynomials in Multidimensional Systems Theory. 6. Hilbert Transform and Spectral Factorization. 7. Conclusions. 8. Updates. 2: Causal and Weakly Causal 2-D Filters with Applications in Stabilization. 1. Scalar 2-D Input / output Systems. 2. Stability. 3. Structural Stability. 4. Multi-Input Multi-Output Systems. 5. Stabilization of Scalar Systems. 6. Characterization of Stabilizers for Scalar Systems. 7. Stabilization of Strictly Causal Transfer Matrices. 8. Characterization of Stabilizers for MIMO Systems. 9. Stabilization of Weakly Causal Systems. 10. Stabilization of MIMO Weakly Causal Systems. 11. Conclusions. 12. Updates. 3: The Equation Ax = b over the Ring C[z, w]. 1. Introduction. 2. Sufficient Condition for Solution. 3. Appendix A. Zero-Dimensional Polynomial Ideals. 4: Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory. 1. Introduction. 2. Gröbner Bases. 3. Algorithmic Construction of Gröbner Bases. 4. An Improved Version of the Algorithm. 5. Application: Canonical Simplification, Decision of Ideal Congruence and Membership, Computation inResidue Class Rings. 6. Application: Solvability and Exact Solution of Systems of Algebraic Equations. 7. Application: Solution of Linear Homogeneous Equations with Polynomial Coefficients. 8. Gröbner Bases for Polynomial Ideals over the Integers. 9. Other Applications. 10. Specializations, Generalizations, Implementations, Complexity. 11. Updates. 5: Multivariate Polynomials, Matrices,and Matrix-Fraction Descriptions. 1. Introduction. 2. Relative Primeness and GCD Extraction from Multivariate Polynomials. 3. Polynomial Matrix Primitive Factorization in the Bivariate Case. 4. Multivariate Polynomial Matrix Factorization. 5. Computations for Coprimeness Using Gröbner Bases. 6. Generalization of the Serre Conjecture and its Consequences. 7. Factorization as a Product of Elementary Matrix Factors. 8. Applications in Multidimensional Systems Stabilization. 9. Behavioral Approach. 10. Conclusions. 6: Recent Impacts of Multidimensional Systems Research. 1. Introduction. 2. Inference of Stability of Sets of Multidimensional Systems from Subsets of Low Cardinality. 3. Multiple Deconvolution Operators for Robust Superresolution. 4. Multisensor Array-Based Superresolution. 5. Wavelets for Superresolution. 6. Other Recent Applications. 7. Conclusions. 7: Multivariate Rational Approximants of the Padé Type. 1. Introduction and Motivation. 2. Multivariate Padé-Type Approximants (Scalar Case). 3. Padé Type Matrix Approximants. 4. Conclusions.

Reviews

From the reviews of the second edition: This new edition presents new results and streamlines the topics. ! There are 352 references and an index. This is a valuable book being both introductory in nature and oriented towards recent developments. (A. Akutowicz, Zentralblatt MATH, Vol. 1046 (21), 2004)

From the reviews of the second edition: <p> This new edition presents new results and streamlines the topics. a ] There are 352 references and an index. This is a valuable book being both introductory in nature and oriented towards recent developments. (A. Akutowicz, Zentralblatt MATH, Vol. 1046 (21), 2004)

From the reviews of the second edition: This new edition presents new results and streamlines the topics. ... There are 352 references and an index. This is a valuable book being both introductory in nature and oriented towards recent developments. (A. Akutowicz, Zentralblatt MATH, Vol. 1046 (21), 2004)

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions