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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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