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ALTERNATIVE APPROACHES

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/9780198527688.003.0008
Subject:
Mathematics, Numerical Analysis

Alternative numerical approaches for solving matrix equations associated with M/G/1-type Markov chains are considered in this chapter. A general shift technique for accelerating the convergence of ... More


Smoothness and Asymptotic Smoothness

Joram Lindenstrauss, David Preiss, and Tiˇser Jaroslav

in Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153551
eISBN:
9781400842698
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153551.003.0008
Subject:
Mathematics, Analysis

This chapter describes the modulus of smoothness of a function in the direction of a family of subspaces and the much simpler notion of upper Fréchet differentiability. It also considers the notion ... More


Porosity, Γ‎N- and Γ‎-Null Sets

Joram Lindenstrauss, David Preiss, and Tiˇser Jaroslav

in Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153551
eISBN:
9781400842698
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153551.003.0010
Subject:
Mathematics, Analysis

This chapter introduces the notion of porosity “at infinity” (formally defined as porosity with respect to a family of subspaces) and discusses the main result, which shows that sets porous with ... More


Efficient Computations

Lars Peter Hansen and Thomas J. Sargent

in Recursive Models of Dynamic Linear Economies

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691042770
eISBN:
9781400848188
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691042770.003.0003
Subject:
Economics and Finance, History of Economic Thought

This chapter describes fast algorithms for computing the value function and optimal decision rule for the type of social planning problem to be described in Chapter 5. The chapter is organized as ... More


Krylov Subspace Methods: Principles and Analysis

Jörg Liesen and Zdenek Strakos

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199655410
eISBN:
9780191744174
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199655410.001.0001
Subject:
Mathematics, Applied Mathematics, Algebra

This book offers a detailed treatment of the mathematical theory of Krylov subspace methods with focus on solving systems of linear algebraic equations. Starting from the idea of projections, Krylov ... More


Introduction

Jörg Liesen and Zdenek Strakos

in Krylov Subspace Methods: Principles and Analysis

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199655410
eISBN:
9780191744174
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199655410.003.0001
Subject:
Mathematics, Applied Mathematics, Algebra

The Introduction consists of three sections that establish the general setting and give background information that is useful to know before starting to read the other chapters. In particular, it ... More


Direct Density-Ratio Estimation with Dimensionality Reduction

Masashi Sugiyama and Motoaki Kawanabe

in Machine Learning in Non-Stationary Environments: Introduction to Covariate Shift Adaptation

Published in print:
2012
Published Online:
September 2013
ISBN:
9780262017091
eISBN:
9780262301220
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262017091.003.0005
Subject:
Computer Science, Machine Learning

This chapter discusses a dimensionality reduction scheme for density-ratio estimation, called direct density-ratio estimation with dimensionality reduction (D3; pronounced as “D-cube”). The basic ... More


The Standard Metric

Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss

in Descent in Buildings (AM-190)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.003.0026
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents some results about groups generated by reflections and the standard metric on a Bruhat-Tits building. It begins with definitions relating to an affine subspace, an affine ... More


Solution of discrete convection–diffusion problems

A. M. Stuart and E. Söli

in Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics

Published in print:
2014
Published Online:
September 2014
ISBN:
9780199678792
eISBN:
9780191780745
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199678792.003.0008
Subject:
Mathematics, Numerical Analysis, Computational Mathematics / Optimization

This chapter concerns iterative methods for solution of discrete convection–diffusion equations. It discusses Krylov subspace methods, principally the generalized minimum residual method, together ... More


Linear symplectic geometry

Dusa McDuff and Dietmar Salamon

in Introduction to Symplectic Topology

Published in print:
2017
Published Online:
June 2017
ISBN:
9780198794899
eISBN:
9780191836411
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198794899.003.0003
Subject:
Mathematics, Analysis, Geometry / Topology

The second chapter introduces the basic concepts of symplectic topology in the linear algebra setting, such as symplectic vector spaces, the linear symplectic group, Lagrangian subspaces, and the ... More


Subspaces and Substructures; Straightness and Differentiability

Tim Maudlin

in New Foundations for Physical Geometry: The Theory of Linear Structures

Published in print:
2014
Published Online:
April 2014
ISBN:
9780198701309
eISBN:
9780191771613
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198701309.003.0007
Subject:
Philosophy, Logic/Philosophy of Mathematics

Parts of spaces are themselves spaces with their own geometrical structure. The way that the part of a space inherits its geometry from an embedding space in the Theory of Linear Structures is ... More


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