eBook ISBN:  9780821876329 
Product Code:  CONM/47.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821876329 
Product Code:  CONM/47.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 47; 1985; 506 ppMSC: Primary 00; Secondary 15; 65; 93
This collection of 35 papers, resulting from the 1984 AMSIMSSIAM Summer Research Conference, displays the crossdevelopments between linear algebra (including numerical linear algebra) and systems and control theory. Linear algebraists will see how some beautiful and strong results of control and systems theory can be derived using the concepts of linear algebra; control and systems theorists will find numerically viable algorithms which can be developed for some important control problems. A full appreciation of the material requires an advanced course in linear algebra, a basic course in matrix computation, and a first course in control theory.

Table of Contents

Articles

Abraham Berman and Daniel Hershkowitz — Graph theoretical methods in studying stability [ MR 828288 ]

M. W. Berry and Robert J. Plemmons — Computing a Banded Basis of the Null Space on the Denelcor HEP Multiprocessor

N. K. Bose — A systemtheoretic approach to stability of sets of polynomials [ MR 828290 ]

Ralph Byers — Numerical condition of the algebraic Riccati equation [ MR 828291 ]

Stephen L. Campbell — Rank deficient least squares and the numerical solution of linear singular implicit systems of differential equations [ MR 828292 ]

J. Casti — Linear methods for nonlinear problems [ MR 828293 ]

G. Conte and A. M. Perdon — Zero modules and factorization problems [ MR 828294 ]

Biswa Nath Datta and Karabi Datta — Sequential and parallel computations and complexities for determining relative primeness, stability and inertia [ MR 828295 ]

Vera W. de Spinadel — On optimal control [ MR 828296 ]

David A. Field — The focal point method and almost linear systems of equations [ MR 828297 ]

Shmuel Friedland — Classification of linear systems [ MR 828298 ]

Paul A. Fuhrmann — On the partial realization problem and the recursive inversion of Hankel and Toeplitz matrices [ MR 828299 ]

Bijoy K. Ghosh — Some Recent Results in Simultaneous System Design

R. E. Hartwig, F. J. Hall and I. J. Katz — Block striped and block nested matrices [ MR 828301 ]

Daniel Hershkowitz and Hans Schneider — Semistability factors and semifactors [ MR 828302 ]

D. Hinrichsen and D. PrätzelWolters — State and input transformations for reachable systems—a polynomial approach [ MR 828303 ]

T. Kailath and H. LevAri — On mappings between covariance matrices and physical systems [ MR 828304 ]

J. Kautsky and N. K. Nichols — Robust multiple eigenvalue assignment by state feedback in linear systems [ MR 828305 ]

L. H. Keel, J. A. Fleming and S. P. Bhattacharyya — Minimum norm pole assignment via Sylvester’s equation [ MR 828306 ]

M. F. Silva Leite — The uniform finite generation problem of Lie groups and its application to control systems [ MR 828307 ]

L. Lerer and M. Tismenetsky — On the location of spectrum of matrix polynomials [ MR 828308 ]

Raphael Loewy — Two matrices which have equal corresponding principal minors [ MR 828309 ]

Michael Neumann and Ronald J. Stern — Cone Reachability for Differential Systems

Christopher C. Paige — Covariance matrix representation in linear filtering [ MR 828311 ]

R. V. Patel — A condensed form for linear systems over principal ideal domains [ MR 828312 ]

T. E. S. Ragahavan — On Pairs of Multidimensional Matrices and Their Applications

Mark A. Shayman — Parametrization of the flags fixed by a unipotent matrix [ MR 828314 ]

Eduardo D. Sontag — An introduction to the stabilization problem for parametrized families of linear systems [ MR 828315 ]

Robert C. Thompson — Smith invariants of a product of integral matrices [ MR 828316 ]

George Trapp — The Riccati equation and the geometric mean [ MR 828317 ]

Paul M. Van Dooren and Michel Verhaegen — On the use of unitary statespace transformations [ MR 828318 ]

Charles Van Loan — How near is a stable matrix to an unstable matrix? [ MR 828319 ]

Jan C. Willems — An approach to exact and approximate modeling of time series [ MR 828320 ]

Harald K. Wimmer — Straight bases of finite abelian groups and a Jordan factorization theorem for integer matrices [ MR 828321 ]

Bostwick F. Wyman and Michael K. Sain — Poles, zeros, and lattices [ MR 828322 ]


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This collection of 35 papers, resulting from the 1984 AMSIMSSIAM Summer Research Conference, displays the crossdevelopments between linear algebra (including numerical linear algebra) and systems and control theory. Linear algebraists will see how some beautiful and strong results of control and systems theory can be derived using the concepts of linear algebra; control and systems theorists will find numerically viable algorithms which can be developed for some important control problems. A full appreciation of the material requires an advanced course in linear algebra, a basic course in matrix computation, and a first course in control theory.

Articles

Abraham Berman and Daniel Hershkowitz — Graph theoretical methods in studying stability [ MR 828288 ]

M. W. Berry and Robert J. Plemmons — Computing a Banded Basis of the Null Space on the Denelcor HEP Multiprocessor

N. K. Bose — A systemtheoretic approach to stability of sets of polynomials [ MR 828290 ]

Ralph Byers — Numerical condition of the algebraic Riccati equation [ MR 828291 ]

Stephen L. Campbell — Rank deficient least squares and the numerical solution of linear singular implicit systems of differential equations [ MR 828292 ]

J. Casti — Linear methods for nonlinear problems [ MR 828293 ]

G. Conte and A. M. Perdon — Zero modules and factorization problems [ MR 828294 ]

Biswa Nath Datta and Karabi Datta — Sequential and parallel computations and complexities for determining relative primeness, stability and inertia [ MR 828295 ]

Vera W. de Spinadel — On optimal control [ MR 828296 ]

David A. Field — The focal point method and almost linear systems of equations [ MR 828297 ]

Shmuel Friedland — Classification of linear systems [ MR 828298 ]

Paul A. Fuhrmann — On the partial realization problem and the recursive inversion of Hankel and Toeplitz matrices [ MR 828299 ]

Bijoy K. Ghosh — Some Recent Results in Simultaneous System Design

R. E. Hartwig, F. J. Hall and I. J. Katz — Block striped and block nested matrices [ MR 828301 ]

Daniel Hershkowitz and Hans Schneider — Semistability factors and semifactors [ MR 828302 ]

D. Hinrichsen and D. PrätzelWolters — State and input transformations for reachable systems—a polynomial approach [ MR 828303 ]

T. Kailath and H. LevAri — On mappings between covariance matrices and physical systems [ MR 828304 ]

J. Kautsky and N. K. Nichols — Robust multiple eigenvalue assignment by state feedback in linear systems [ MR 828305 ]

L. H. Keel, J. A. Fleming and S. P. Bhattacharyya — Minimum norm pole assignment via Sylvester’s equation [ MR 828306 ]

M. F. Silva Leite — The uniform finite generation problem of Lie groups and its application to control systems [ MR 828307 ]

L. Lerer and M. Tismenetsky — On the location of spectrum of matrix polynomials [ MR 828308 ]

Raphael Loewy — Two matrices which have equal corresponding principal minors [ MR 828309 ]

Michael Neumann and Ronald J. Stern — Cone Reachability for Differential Systems

Christopher C. Paige — Covariance matrix representation in linear filtering [ MR 828311 ]

R. V. Patel — A condensed form for linear systems over principal ideal domains [ MR 828312 ]

T. E. S. Ragahavan — On Pairs of Multidimensional Matrices and Their Applications

Mark A. Shayman — Parametrization of the flags fixed by a unipotent matrix [ MR 828314 ]

Eduardo D. Sontag — An introduction to the stabilization problem for parametrized families of linear systems [ MR 828315 ]

Robert C. Thompson — Smith invariants of a product of integral matrices [ MR 828316 ]

George Trapp — The Riccati equation and the geometric mean [ MR 828317 ]

Paul M. Van Dooren and Michel Verhaegen — On the use of unitary statespace transformations [ MR 828318 ]

Charles Van Loan — How near is a stable matrix to an unstable matrix? [ MR 828319 ]

Jan C. Willems — An approach to exact and approximate modeling of time series [ MR 828320 ]

Harald K. Wimmer — Straight bases of finite abelian groups and a Jordan factorization theorem for integer matrices [ MR 828321 ]

Bostwick F. Wyman and Michael K. Sain — Poles, zeros, and lattices [ MR 828322 ]