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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 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


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


SPECTRALLY CONSTRAINED APPROXIMATION

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/9780198566649.003.0007
Subject:
Mathematics, Applied Mathematics

This chapter shows that the problems of computing least squares approximations for various types of real and symmetric matrices subject to spectral constraints share a common structure. A general ... More


STRUCTURED LOW RANK APPROXIMATION

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/9780198566649.003.0008
Subject:
Mathematics, Applied Mathematics

The task of retrieving useful information while maintaining the underlying physical feasibility often necessitates the search for a good structured lower rank approximation of the data matrix. This ... More


Toeplitz Operators and Hitchin's Projectively Flat Connection

Jørgen Ellegaard Andersen

in The Many Facets of Geometry: A Tribute to Nigel Hitchin

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199534920
eISBN:
9780191716010
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534920.003.0010
Subject:
Mathematics, Geometry / Topology

This chapter reviews some of the results that have been established regarding representations of the mapping class group and the curve operators. It discusses the geometric construction of these ... More


The Ising model in two dimensions: summary of results

Barry M. McCoy

in Advanced Statistical Mechanics

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199556632
eISBN:
9780191723278
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556632.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter summarizes the many results of the exactly solved Ising model in two dimensions at H = 0 including: the partition function, free energy, spontaneous magnetization, the Toeplitz ... More


Completions of positive semidefinite operator matrices

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/9780691128894.003.0002
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter deals with positive definite and semidefinite completions of partial operator matrices. It considers the banded case in Section 2.1, the chordal case in Section 2.2, the Toeplitz case in ... 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


The Hilbert Transform on Lp(T) and Riesz’s Theorem

Ali Taheri

in Function Spaces and Partial Differential Equations: Volume 1 - Classical Analysis

Published in print:
2015
Published Online:
September 2015
ISBN:
9780198733133
eISBN:
9780191797712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198733133.003.0007
Subject:
Mathematics, Analysis

This chapter introduces the conjugate or Hilbert transform on the circle and establishes its a.e. existence and Lp boundedness by three different methods. The chapter also includes an application of ... More


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