11 
Spectral properties of combinatorial classes of matricesKim, InJae. January 2005 (has links)
Thesis (Ph. D.)University of Wyoming, 2005. / Title from PDF title page (viewed on Feb. 22, 2008). Includes bibliographical references (p. 136139).

12 
A Hecke ring of split reductive groups over a number fieldBruggeman, Roelof Wichert. January 1972 (has links)
ThesisRijksunivers teit te Utrecht. / Includes bibliographical references (p. 103104).

13 
Aspects of Toeplitz operators and matrices : asymptotics, norms, singular values / Hermann RabeRabe, Hermann January 2015 (has links)
The research contained in this thesis can be divided into two related, but distinct parts.
The rst chapter deals with block Toeplitz operators de ned by rational matrix function
symbols on discrete sequence spaces. Here we study sequences of operators that converge
to the inverses of these Toeplitz operators via an invertibility result involving a special
representation of the symbol of these block Toeplitz operators. The second part focuses on
a special class of matrices generated by banded Toeplitz matrices, i.e., Toeplitz matrices
with a nite amount of nonzero diagonals. The spectral theory of banded Toeplitz
matrices is well developed, and applied to solve questions regarding the behaviour of
the singular values of Toeplitzgenerated matrices. In particular, we use the behaviour
of the singular values to deduce bounds for the growth of the norm of the inverse of
Toeplitzgenerated matrices.
In chapter 2, we use a special statespace representation of a rational matrix function
on the unit circle to de ne a block Toeplitz operator on a discrete sequence space. A
discrete Riccati equation can be associated with this representation which can be used
to prove an invertibility theorem for these Toeplitz operators. Explicit formulas for the
inverse of the Toeplitz operators are also derived that we use to de ne a sequence of
operators that converge in norm to the inverse of the Toeplitz operator. The rate of
this convergence, as well as that of a related Riccati di erence equation is also studied.
We conclude with an algorithm for the inversion of the nite sections of block Toeplitz
operators.
Chapter 3 contains the main research contribution of this thesis. Here we derive
sharp growth rates for the norms of the inverses of Toeplitzgenerated matrices. These
results are achieved by employing powerful theory related to the AvramParter theorem
that describes the distribution of the singular values of banded Toeplitz matrices. The
investigation is then extended to include the behaviour of the extreme and general singular
values of Toeplitzgenerated matrices.
We conclude with Chapter 4, which sets out to answer a very speci c question regarding
the singular vectors of a particular subclass of Toeplitzgenerated matrices. The
entries of each singular vector seems to be a permutation (up to sign) of the same set
of real numbers. To arrive at an explanation for this phenomenon, explicit formulas are
derived for the singular values of the banded Toeplitz matrices that serve as generators
for the matrices in question. Some abstract algebra is also employed together with some
results from the previous chapter to describe the permutation phenomenon. Explicit
formulas are also shown to exist for the inverses of these particular Toeplitzgenerated
matrices as well as algorithms to calculate the norms and norms of the inverses. Finally,
some additional results are compiled in an appendix. / PhD (Mathematics), NorthWest University, Potchefstroom Campus, 2015

14 
Aspects of Toeplitz operators and matrices : asymptotics, norms, singular values / Hermann RabeRabe, Hermann January 2015 (has links)
The research contained in this thesis can be divided into two related, but distinct parts.
The rst chapter deals with block Toeplitz operators de ned by rational matrix function
symbols on discrete sequence spaces. Here we study sequences of operators that converge
to the inverses of these Toeplitz operators via an invertibility result involving a special
representation of the symbol of these block Toeplitz operators. The second part focuses on
a special class of matrices generated by banded Toeplitz matrices, i.e., Toeplitz matrices
with a nite amount of nonzero diagonals. The spectral theory of banded Toeplitz
matrices is well developed, and applied to solve questions regarding the behaviour of
the singular values of Toeplitzgenerated matrices. In particular, we use the behaviour
of the singular values to deduce bounds for the growth of the norm of the inverse of
Toeplitzgenerated matrices.
In chapter 2, we use a special statespace representation of a rational matrix function
on the unit circle to de ne a block Toeplitz operator on a discrete sequence space. A
discrete Riccati equation can be associated with this representation which can be used
to prove an invertibility theorem for these Toeplitz operators. Explicit formulas for the
inverse of the Toeplitz operators are also derived that we use to de ne a sequence of
operators that converge in norm to the inverse of the Toeplitz operator. The rate of
this convergence, as well as that of a related Riccati di erence equation is also studied.
We conclude with an algorithm for the inversion of the nite sections of block Toeplitz
operators.
Chapter 3 contains the main research contribution of this thesis. Here we derive
sharp growth rates for the norms of the inverses of Toeplitzgenerated matrices. These
results are achieved by employing powerful theory related to the AvramParter theorem
that describes the distribution of the singular values of banded Toeplitz matrices. The
investigation is then extended to include the behaviour of the extreme and general singular
values of Toeplitzgenerated matrices.
We conclude with Chapter 4, which sets out to answer a very speci c question regarding
the singular vectors of a particular subclass of Toeplitzgenerated matrices. The
entries of each singular vector seems to be a permutation (up to sign) of the same set
of real numbers. To arrive at an explanation for this phenomenon, explicit formulas are
derived for the singular values of the banded Toeplitz matrices that serve as generators
for the matrices in question. Some abstract algebra is also employed together with some
results from the previous chapter to describe the permutation phenomenon. Explicit
formulas are also shown to exist for the inverses of these particular Toeplitzgenerated
matrices as well as algorithms to calculate the norms and norms of the inverses. Finally,
some additional results are compiled in an appendix. / PhD (Mathematics), NorthWest University, Potchefstroom Campus, 2015

15 
Generalized Feature Embedding Learning for Clustering and ClassicationUnknown Date (has links)
Data comes in many di erent shapes and sizes. In real life applications it is
common that data we are studying has features that are of varied data types. This
may include, numerical, categorical, and text. In order to be able to model this data
with machine learning algorithms, it is required that the data is typically in numeric
form. Therefore, for data that is not originally numerical, it must be transformed to
be able to be used as input into these algorithms.
Along with this transformation it is common that data we study has many
features relative to the number of samples in the data. It is often desirable to reduce
the number of features that are being trained in a model to eliminate noise and reduce
time in training. This problem of high dimensionality can be approached through
feature selection, feature extraction, or feature embedding. Feature selection seeks to
identify the most essential variables in a dataset that will lead to a parsimonious model
and high performing results, while feature extraction and embedding are techniques
that utilize a mathematical transformation of the data into a represented space. As a
byproduct of using a new representation, we are able to reduce the dimension greatly
without sacri cing performance. Oftentimes, by using embedded features we observe a gain in performance.
Though extraction and embedding methods may be powerful for isolated machine
learning problems, they do not always generalize well. Therefore, we are motivated
to illustrate a methodology that can be applied to any data type with little
preprocessing. The methods we develop can be applied in unsupervised, supervised,
incremental, and deep learning contexts. Using 28 benchmark datasets as examples
which include di erent data types, we construct a framework that can be applied for
general machine learning tasks.
The techniques we develop contribute to the eld of dimension reduction and
feature embedding. Using this framework, we make additional contributions to eigendecomposition
by creating an objective matrix that includes three main vital components.
The rst being a class partitioned row and feature product representation
of onehot encoded data. Secondarily, the derivation of a weighted adjacency matrix
based on class label relationships. Finally, by the inner product of these aforementioned
values, we are able to condition the onehot encoded data generated from the
original data prior to eigenvector decomposition. The use of class partitioning and
adjacency enable subsequent projections of the data to be trained more e ectively
when compared sidetoside to baseline algorithm performance. Along with this improved
performance, we can adjust the dimension of the subsequent data arbitrarily.
In addition, we also show how these dense vectors may be used in applications to
order the features of generic data for deep learning.
In this dissertation, we examine a general approach to dimension reduction and
feature embedding that utilizes a class partitioned row and feature representation, a
weighted approach to instance similarity, and an adjacency representation. This general
approach has application to unsupervised, supervised, online, and deep learning.
In our experiments of 28 benchmark datasets, we show signi cant performance gains
in clustering, classi cation, and training time. / Includes bibliography. / Dissertation (Ph.D.)Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

16 
Extensions of principal components analysisBrubaker, S. Charles. January 2009 (has links)
Thesis (Ph.D)Computing, Georgia Institute of Technology, 2009. / Committee Chair: Santosh Vempala; Committee Member: Adam Kalai; Committee Member: Haesun Park; Committee Member: Ravi Kannan; Committee Member: Vladimir Koltchinskii. Part of the SMARTech Electronic Thesis and Dissertation Collection.

17 
Nonperturbative renormalization and low mode averaging with domain wall fermionsArthur, Rudy January 2012 (has links)
This thesis presents an improved method to calculate renormalization constants in a regularization invariant momentum scheme using twisted boundary conditions. This enables us to simulate with momenta of arbitrary magnitude and a fixed direction. With this new technique, together with nonexceptional kinematics and volume sources, we are able to take a statistically and theoretically precise continuum limit. Thereafter, all the running of the operators with momentum scale is due to their anomalous dimension. We use this to develop a practical scheme for step scaling with off shell vertex functions. We develop the method on 16³ × 32 lattices to show the practicality of using small volume simulations to step scale to high momenta. We also use larger 24³×64 and 32³×64 lattices to compute renormalization constants very accurately. Combining these with previous analyses we are able to extract a precise value for the light and strange quark masses and the neutral kaon mixing parameter BK. We also analyse eigenvectors of the domain wall Dirac matrix. We develop a practical and cost effective way to compute eigenvectors using the implicitly restarted Lanczos method with Chebyshev acceleration. We show that calculating eigenvectors to accelerate propagator inversions is cost effective when as few as one or two propagators are required. We investigate the technique of low mode averaging (LMA) with eigenvectors of the domain wall matrix for the first time. We find that for low energy correlators, pions for example, LMA is very effective at reducing the statistical noise. We also calculated the η and η′ meson masses, which required evaluating disconnected correlation functions and combining stochastic sources with LMA.

18 
Behavioral specifications of network autocorrelation in migration modeling an analysis of migration flows by spatial filtering /Chun, Yongwan, January 2007 (has links)
Thesis (Ph. D.)Ohio State University, 2007. / Full text release at OhioLINK's ETD Center delayed at author's request

19 
Students' transfer of learning of eigenvalues and eigenvectors : implementation of actororiented transfer framework /Karakök, Gülden. January 1900 (has links)
Thesis (Ph. D.)Oregon State University, 2009. / Printout. Includes bibliographical references (leaves 298303). Also available on the World Wide Web.

20 
Methods for solving large symmetric eigenvalue problems associated with configuration interaction electronic structure calulations /Maschhoff, Kristyn Joy, January 1994 (has links)
Thesis (Ph. D.)University of Washington, 1994. / Vita. Includes bibliographical references (leaves [139]141).

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