Jump to ContentJump to Main Navigation

You are looking at 1-20 of 27 items

  • Keywords: eigenvalue x
Clear All Modify Search

View:

LEAST SQUARES 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/9780198566649.003.0006
Subject:
Mathematics, Applied Mathematics

Every inverse eigenvalue problem has a natural generalization to a least squares formulation, which sometimes does carry significant purposes in applications. The least squares approximation can be ... 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


Classic Food Web Theory

Kevin S. McCann

in Food Webs (MPB-50)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691134178
eISBN:
9781400840687
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691134178.003.0010
Subject:
Biology, Ecology

This chapter examines the basic assumptions of classic food web theory. It first considers the classic whole-community approach, which assumes that any specific matrix represents a sample from a ... More


Solving Nonlinear Rational Expectations Models by Eigenvalue–Eigenvector Decompositions

Alfonso Novales, Emilio Domínguez, Javier J. Pérez, and Jesús Ruiz

in Computational Methods for the Study of Dynamic Economies

Published in print:
2001
Published Online:
November 2003
ISBN:
9780199248278
eISBN:
9780191596605
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199248273.003.0004
Subject:
Economics and Finance, Macro- and Monetary Economics

Discusses the main issues involved in practical applications of solution methods that have been proposed for rational expectations models, based on eigenvalue–eigenvector decompositions. It starts by ... More


Matrix Mechanics

Gary E. Bowman

in Essential Quantum Mechanics

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199228928
eISBN:
9780191711206
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199228928.003.0006
Subject:
Physics, Condensed Matter Physics / Materials

This chapter introduces the matrix-mechanics formulation of quantum mechanics, emphasizing both calculational techniques and conceptual understanding. Parallels between matrix mechanics and ordinary ... More


Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

Klaus Boehmer

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577040
eISBN:
9780191595172
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577040.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, and create an exciting interplay. Other books discuss nonlinearity by a very few important ... More


Nonconforming finite element methods

Klaus Böhmer

in Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577040
eISBN:
9780191595172
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577040.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Nonconforming FEMs avoid the strong restrictions of conforming FEMs. So discontinuous ansatz and test functions, approximate test integrals, and strong forms are admitted. This allows the proof of ... More


Critique of the Standard Interpretation

Bas C. van Fraassen

in Quantum Mechanics: An Empiricist View

Published in print:
1991
Published Online:
November 2003
ISBN:
9780198239802
eISBN:
9780191597466
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198239807.003.0008
Subject:
Philosophy, Philosophy of Science

Von Neumann's unification of Schroedinger's and Heisenberg's formalisms came with an interpretation of quantum theory involving two principles. The first is that assertions about the values of ... More


Modal Interpretation of Quantum Mechanics 1

Bas C. van Fraassen

in Quantum Mechanics: An Empiricist View

Published in print:
1991
Published Online:
November 2003
ISBN:
9780198239802
eISBN:
9780191597466
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198239807.003.0009
Subject:
Philosophy, Philosophy of Science

The world of quantum theory is not deterministic; however, the quantum theory of an isolated system describes its state as evolving deterministically.How can these two points be reconciled? The modal ... More


Small Vibrations About Equilibrium

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0010
Subject:
Physics, Atomic, Laser, and Optical Physics

A number of interesting mechanical systems have one or more essentially stable equilibrium configurations. When disturbed slightly, they vibrate about equilibrium in characteristic patterns called ... More


The Bare Theory and Determinate Experience

Jeffrey Alan Barrett

in The Quantum Mechanics of Minds and Worlds

Published in print:
2001
Published Online:
March 2012
ISBN:
9780199247431
eISBN:
9780191697661
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199247431.003.0004
Subject:
Philosophy, Philosophy of Science, Metaphysics/Epistemology

This chapter begins by discussing several strategies for interpreting the global state. Next, it explains that the bare theory is simply the standard von Neumann–Dirac formulation of quantum ... More


Abstract Hilbert Space

John von Neumann

Nicholas A. Wheeler (ed.)

in Mathematical Foundations of Quantum Mechanics: New Edition

Published in print:
2018
Published Online:
September 2018
ISBN:
9780691178561
eISBN:
9781400889921
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691178561.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter defines Hilbert space, which furnishes the mathematical basis for the treatment of quantum mechanics. This is done within the context of an equation introduced in the previous chapter, ... More


Well Posedness

G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos

in Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691142173
eISBN:
9781400842650
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142173.003.0004
Subject:
Mathematics, Applied Mathematics

This chapter presents rigorous mathematical results concerning the solvability and well posedness of time-harmonic problems for complex electromagnetic media, with a special emphasis on chiral media. ... More


The Anisotropic Heisenberg Quantum Spin Chain

Hans-Peter Eckle

in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

Published in print:
2019
Published Online:
September 2019
ISBN:
9780199678839
eISBN:
9780191878589
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199678839.003.0013
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

This chapter introduces the Heisenberg model, a fully quantum mechanical model that describes the magnetism of localized magnetic moments. The one-dimensional version of the Heisenberg model, the ... More


Electronic Systems

Hans-Peter Eckle

in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

Published in print:
2019
Published Online:
September 2019
ISBN:
9780199678839
eISBN:
9780191878589
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199678839.003.0016
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

The Bethe ansatz can be generalized to problems where particles have internal degrees of freedom. The generalized method can be viewed as two Bethe ansätze executed one after the other: nested Bethe ... More


Linear Elliptic Equations

Rüdiger Verfürth

in A Posteriori Error Estimation Techniques for Finite Element Methods

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199679423
eISBN:
9780191758485
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199679423.003.0004
Subject:
Mathematics, Applied Mathematics, Numerical Analysis

We establish a posteriori error estimates for the discretisation of linear elliptic equations departing from a general abstract framework which accentuates the generic equivalence of the error to the ... More


Nonlinear Elliptic Equations

Rüdiger Verfürth

in A Posteriori Error Estimation Techniques for Finite Element Methods

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199679423
eISBN:
9780191758485
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199679423.003.0005
Subject:
Mathematics, Applied Mathematics, Numerical Analysis

We present a posteriori error estimates for nonlinear stationary problems departing from an abstract result which establishes the basic equivalence of error and residual. The main tool is the ... More


Transformations, matrices and operators

Chun Wa Wong

in Introduction to Mathematical Physics: Methods & Concepts

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199641390
eISBN:
9780191747786
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641390.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Linear algebra of matrices is discussed in the context of rotations in space. Determinants are used to find solutions of simultaneous linear equations, to invert matrices and to find matrix ... More


Networks

Stefan Thurner, Rudolf Hanel, and Peter Klimekl

in Introduction to the Theory of Complex Systems

Published in print:
2018
Published Online:
November 2018
ISBN:
9780198821939
eISBN:
9780191861062
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198821939.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Understanding the interactions between the components of a system is key to understanding it. In complex systems, interactions are usually not uniform, not isotropic and not homogeneous: each ... More


Entropy Numbers, s-Numbers, and Eigenvalues

D. E. Edmunds and W. D. Evans

in Spectral Theory and Differential Operators

Published in print:
2018
Published Online:
September 2018
ISBN:
9780198812050
eISBN:
9780191861130
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198812050.003.0002
Subject:
Mathematics, Pure Mathematics

The geometric quantities entropy numbers, approximation numbers and n-widths are defined for compact linear maps, and connections with the analytic entities eigenvalues and essential spectra ... More


View: