Series 
Springer monographs in mathematics 

Springer monographs in mathematics.

Subject 
Complex matrices.


Matrices.


Eigenvalues.


Spectral theory (Mathematics)


Differentiable dynamical systems.


Neural networks (Computer science)

Alt Name 
Webb, Benjamin (Benjamin Z.),

Description 
1 online resource. 
Bibliography Note 
Includes bibliographical references and index. 
Contents 
Isospectral Transformations: A New Approach to Analyzing Multidimensional Systems and Networks  Isospectral Matrix Reductions  Dynamical Networks and Isospectral Graph Reductions  Stability of Dynamical Networks  Improved Eigenvalue Estimates  Pseudospectra and Inverse Pseudospectra  Improved Estimates of Survival Probabilities. 
Summary 
This book presents a new approach to the analysis of networks, which emphasizes how one can compress a network while preserving all information relative to the network's spectrum. This approach can be applied to any network irrespective of the network's structure or whether the network is directed, undirected, weighted, unweighted, etc. Besides these compression techniques, the authors introduce a number of other isospectral transformations and demonstrate how, together, these methods can be applied to gain new results in a number of areas. This includes the stability of timedelayed and non timedelayed dynamical networks, eigenvalue estimation, pseudospectra analysis, and the estimation of survival probabilities in open dynamical systems. The theory of isospectral transformations, developed in this text, can be readily applied in any area that involves the analysis of multidimensional systems and is especially applicable to the analysis of network dynamics. This book will be of interest to mathematicians, physicists, biologists, engineers and to anyone who has an interest in the dynamics of networks. 
Note 
Print version record. 
ISBN 
9781493913756 (electronic bk.) 

1493913751 (electronic bk.) 

9781493913749 

1493913743 
ISBN/ISSN 
10.1007/9781493913756 
OCLC # 
890469491 
Additional Format 
Print version: Bunimovich, Leonid. Isospectral transformations 1493913743 (OCoLC)880965528 
