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STRUCTURED MATRIX ANALYSIS

D. A. Bini, G. Latouche, and B. Meini

in Numerical Methods for Structured Markov Chains

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.003.0002
Subject:
Mathematics, Numerical Analysis

This chapter describes structural and computational properties which are the basis of the design and analysis of fast algorithms for the numerical solution of structured Markov chains. Toeplitz ... More


MATRIX EQUATIONS AND CANONICAL FACTORIZATIONS

D. A. Bini, G. Latouche, and B. Meini

in Numerical Methods for Structured Markov Chains

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.003.0003
Subject:
Mathematics, Numerical Analysis

This chapter is concerned with infinite block Toeplitz matrices, their relationships with matrix power series and matrix Laurent power series, and the fundamental problem of solving matrix equations ... More


Numerical Methods for Structured Markov Chains

Dario A. Bini, Guy Latouche, and Beatrice Meini

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.001.0001
Subject:
Mathematics, Numerical Analysis

The book deals with the numerical solution of structured Markov chains which include M/G/1 and G/M/1-type Markov chains, QBD processes, non-skip-free queues, and tree-like stochastic processes and ... More


STRUCTURED INVERSE EIGENVALUE PROBLEMS

Moody T. Chu and Gene H. Golub

in Inverse Eigenvalue Problems: Theory, Algorithms, and Applications

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566649
eISBN:
9780191718021
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566649.003.0004
Subject:
Mathematics, Applied Mathematics

The feasibility conditions for a physical system often mandate specific structural stipulations on the inverse problems. This chapter focuses on eight selected structures: Jacobi matrices, Toeplitz ... More


PARTIALLY DESCRIBED INVERSE EIGENVALUE PROBLEMS

Moody T. Chu and Gene H. Golub

in Inverse Eigenvalue Problems: Theory, Algorithms, and Applications

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566649
eISBN:
9780191718021
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566649.003.0005
Subject:
Mathematics, Applied Mathematics

In practice, it is often the case that only partial information on eigenvalues and eigenvectors is available. In many cases, just a few eigenpairs can determine much of the desirable reconstruction. ... More


Multivariable moments and sums of Hermitian squares

Mihály Bakonyi and Hugo J. Woerdeman

in Matrix Completions, Moments, and Sums of Hermitian Squares

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691128894
eISBN:
9781400840595
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691128894.003.0003
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter shows how five closely related problems become vastly different when one considers the multivariable case. In a similar way, various natural sums of Hermitian squares problems that one ... More


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