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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


Linear Algebra and the Dirac Notation

Phillip Kaye, Raymond Laflamme, and Michele Mosca

in An Introduction to Quantum Computing

Published in print:
2006
Published Online:
November 2020
ISBN:
9780198570004
eISBN:
9780191916724
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198570004.003.0005
Subject:
Computer Science, Computer Architecture and Logic Design

We assume the reader has a strong background in elementary linear algebra. In this section we familiarize the reader with the algebraic notation used in quantum ... More


Introductory Quantum Algorithms

Phillip Kaye, Raymond Laflamme, and Michele Mosca

in An Introduction to Quantum Computing

Published in print:
2006
Published Online:
November 2020
ISBN:
9780198570004
eISBN:
9780191916724
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198570004.003.0009
Subject:
Computer Science, Computer Architecture and Logic Design

In this chapter we will describe some of the early quantum algorithms. These algorithms are simple and illustrate the main ingredients behind the more useful and ... More


Other Applications of Neural Networks to Quantum Mechanical Problems

Lionel Raff, Ranga Komanduri, Martin Hagan, and Satish Bukkapatnam

in Neural Networks in Chemical Reaction Dynamics

Published in print:
2012
Published Online:
November 2020
ISBN:
9780199765652
eISBN:
9780197563113
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199765652.003.0014
Subject:
Chemistry, Physical Chemistry

The usual method for solving the vibrational Schrödinger equation to obtain molecular vibrational spectra and the associated wave functions generally involves the ... More


Demographic Models and Branching Processes

C. Y. Cyrus Chu

in Title Pages

Published in print:
1998
Published Online:
November 2020
ISBN:
9780195121582
eISBN:
9780197561287
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195121582.003.0006
Subject:
Earth Sciences and Geography, Economic Geography

All models describing the dynamic pattern of human population have two common features. First, the human population is usually divided into several types, ... More


Income-Specific Population Models: Steady States and Comparative Dynamics

C. Y. Cyrus Chu

in Population Dynamics: A New Economic Approach

Published in print:
1998
Published Online:
November 2020
ISBN:
9780195121582
eISBN:
9780197561287
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195121582.003.0008
Subject:
Earth Sciences and Geography, Economic Geography

I mentioned in chapter 1 that the standard new household economics model of fertility, derived and modified by Becker (1960), DeTray (1973), Willis (1973), ... More


Lineage Extinction and Inheritance Patterns

C. Y. Cyrus Chu

in Population Dynamics: A New Economic Approach

Published in print:
1998
Published Online:
November 2020
ISBN:
9780195121582
eISBN:
9780197561287
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195121582.003.0009
Subject:
Earth Sciences and Geography, Economic Geography

Perhaps the most basic biological instincts of all creatures are to survive and to produce offspring. In ancient times, poor hygienic environment and ... 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


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