Matching Items (18)
Some topics concerning the singular value decomposition and generalized singular value decomposition
Description
This dissertation involves three problems that are all related by the use of the singular value decomposition (SVD) or generalized singular value decomposition (GSVD). The specific problems are (i) derivation of a generalized singular value expansion (GSVE), (ii) analysis of the properties of the chi-squared method for regularization parameter selection in the case of nonnormal data and (iii) formulation of a partial canonical correlation concept for continuous time stochastic processes. The finite dimensional SVD has an infinite dimensional generalization to compact operators. However, the form of the finite dimensional GSVD developed in, e.g., Van Loan does not extend directly to infinite dimensions as a result of a key step in the proof that is specific to the matrix case. Thus, the first problem of interest is to find an infinite dimensional version of the GSVD. One such GSVE for compact operators on separable Hilbert spaces is developed. The second problem concerns regularization parameter estimation. The chi-squared method for nonnormal data is considered. A form of the optimized regularization criterion that pertains to measured data or signals with nonnormal noise is derived. Large sample theory for phi-mixing processes is used to derive a central limit theorem for the chi-squared criterion that holds under certain conditions. Departures from normality are seen to manifest in the need for a possibly different scale factor in normalization rather than what would be used under the assumption of normality. The consequences of our large sample work are illustrated by empirical experiments. For the third problem, a new approach is examined for studying the relationships between a collection of functional random variables. The idea is based on the work of Sunder that provides mappings to connect the elements of algebraic and orthogonal direct sums of subspaces in a Hilbert space. When combined with a key isometry associated with a particular Hilbert space indexed stochastic process, this leads to a useful formulation for situations that involve the study of several second order processes. In particular, using our approach with two processes provides an independent derivation of the functional canonical correlation analysis (CCA) results of Eubank and Hsing. For more than two processes, a rigorous derivation of the functional partial canonical correlation analysis (PCCA) concept that applies to both finite and infinite dimensional settings is obtained.
ContributorsHuang, Qing (Author) / Eubank, Randall (Thesis advisor) / Renaut, Rosemary (Thesis advisor) / Cochran, Douglas (Committee member) / Gelb, Anne (Committee member) / Young, Dennis (Committee member) / Arizona State University (Publisher)
Created2012
Description
Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.
ContributorsIlkturk, Utku (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Renaut, Rosemary (Committee member) / Armbruster, Dieter (Committee member) / Arizona State University (Publisher)
Created2015
Description航天产业属于技术密集型行业，现阶段中国航天的发展需要巨额资金和科研人力资本。传统航天企业内员工相较商业航天企业缺乏创新精神，“搭便车”现象严重，缺乏以创新为内在增长动力的传统航天产业，其发展持续性终究得不到满足。相比而言，国内外的商业航天企业却展现出较强的创新能力。遗憾的是，虽然航天产业的高科技属性决定了科研人员的关键角色，但目前的研究几乎没有系统地研究过不同的体制对航天产业创新的影响机制，而有限的研究也集中在讨论宏观环境对行业创新的影响。本研究将弥补这方面研究的不足，分析传统航天模式与新兴商业航天模式下科研人员创新力差别的内在动因，力求给传统航天产业的发展提供有实际意义的参考和建议。
作者自2008年加入传统航天院所从事科研工作，2014年创立中国第一家商业卫星公司，在实践中充分利用面试知识型员工的机会，并深入访谈了不同职级的科研人员，覆盖了30家商业航天公司（截至2016年上市公司54家），包括来自中国传统航天的科研院所、直属航天企业及新兴商业航天公司300余人。通过多次沟通、邮件往来等方式进一步调查研究，发现不同所有制公司的员工在组织认同度方面存在较为明显的差异。为了系统科学地理解组织认同度在航天行业内如何影响不同体制下的科研人员的创新，本研究采用问卷调查的形式收集了1200份问卷，研究在传统航天及商业航天这两种不同所有制的航天企业中，组织认同度与科研人员创新能力的关系。从实证结果来看，航天产业员工组织认同度会显著影响员工的创新绩效，组织认同度越高的员工其创新能力往往更强，员工创新绩效越高。与此同时，通过进一步研究分析发现，航天产业公司所有权属性的差异在组织认同影响员工创新能力的过程中起着调节作用。具体而言，传统航天企业中的员工，其组织认同度对其员工创新能力影响更小，商业航天公司员工创新能力受到其组织认同度的影响相对较大。
研究结果从某种程度上反映了航天领域不同所有权属性企业所具有的不同的组织文化、组织价值观与组织结构会导致其员工个体组织认同度对其创新行为的影响产生差异。从组织文化的角度出发，商业航天企业其组织文化相对于传统航天企业而言更加自由，对员工创意、创新行为限制更少，这种自由的文化刺激并提高了员工的组织认同度，使得个体创新行为的效果更加显著。另外，从组织价值观的角度而言，商业航天企业员工相对于传统航天企业员工来讲更加看重创新行为的意义，其对员工创新行为的重视使其员工组织认同度对员工取得创新绩效产生了催化作用。最后，从组织结构的角度来看，商业航天企业其管理层相对而言往往更愿意接受企业中员工的创意与创新行为，给员工留下了相当大的创新空间，这种灵活的管理方式从某种程度上也会促进组织认同度对员工创新行为产生影响。
作者自2008年加入传统航天院所从事科研工作，2014年创立中国第一家商业卫星公司，在实践中充分利用面试知识型员工的机会，并深入访谈了不同职级的科研人员，覆盖了30家商业航天公司（截至2016年上市公司54家），包括来自中国传统航天的科研院所、直属航天企业及新兴商业航天公司300余人。通过多次沟通、邮件往来等方式进一步调查研究，发现不同所有制公司的员工在组织认同度方面存在较为明显的差异。为了系统科学地理解组织认同度在航天行业内如何影响不同体制下的科研人员的创新，本研究采用问卷调查的形式收集了1200份问卷，研究在传统航天及商业航天这两种不同所有制的航天企业中，组织认同度与科研人员创新能力的关系。从实证结果来看，航天产业员工组织认同度会显著影响员工的创新绩效，组织认同度越高的员工其创新能力往往更强，员工创新绩效越高。与此同时，通过进一步研究分析发现，航天产业公司所有权属性的差异在组织认同影响员工创新能力的过程中起着调节作用。具体而言，传统航天企业中的员工，其组织认同度对其员工创新能力影响更小，商业航天公司员工创新能力受到其组织认同度的影响相对较大。
研究结果从某种程度上反映了航天领域不同所有权属性企业所具有的不同的组织文化、组织价值观与组织结构会导致其员工个体组织认同度对其创新行为的影响产生差异。从组织文化的角度出发，商业航天企业其组织文化相对于传统航天企业而言更加自由，对员工创意、创新行为限制更少，这种自由的文化刺激并提高了员工的组织认同度，使得个体创新行为的效果更加显著。另外，从组织价值观的角度而言，商业航天企业员工相对于传统航天企业员工来讲更加看重创新行为的意义，其对员工创新行为的重视使其员工组织认同度对员工取得创新绩效产生了催化作用。最后，从组织结构的角度来看，商业航天企业其管理层相对而言往往更愿意接受企业中员工的创意与创新行为，给员工留下了相当大的创新空间，这种灵活的管理方式从某种程度上也会促进组织认同度对员工创新行为产生影响。
ContributorsWang, Yang (Author) / Zhu, Hongquan (Thesis advisor) / Zhang, Anmin (Thesis advisor) / Zheng, Zhiqiang (Committee member) / Arizona State University (Publisher)
Created2019
Description
A specific species of the genus Geobacter exhibits useful electrical properties when processing a molecule often found in waste water. A team at ASU including Dr Cèsar Torres and Dr Sudeep Popat used that species to create a special type of solid oxide fuel cell we refer to as a microbial fuel cell. Identification of possible chemical processes and properties of the reactions used by the Geobacter are investigated indirectly by taking measurements using Electrochemical Impedance Spectroscopy of the electrode-electrolyte interface of the microbial fuel cell to obtain the value of the fuel cell's complex impedance at specific frequencies. Investigation of the multiple polarization processes which give rise to measured impedance values is difficult to do directly and so examination of the distribution function of relaxation times (DRT) is considered instead. The DRT is related to the measured complex impedance values using a general, non-physical equivalent circuit model. That model is originally given in terms of a Fredholm integral equation with a non-square integrable kernel which makes the inverse problem of determining the DRT given the impedance measurements an ill-posed problem. The original integral equation is rewritten in terms of new variables into an equation relating the complex impedance to the convolution of a function based upon the original integral kernel and a related but separate distribution function which we call the convolutional distribution function. This new convolutional equation is solved by reducing the convolution to a pointwise product using the Fourier transform and then solving the inverse problem by pointwise division and application of a filter function (equivalent to regularization). The inverse Fourier transform is then taken to get the convolutional distribution function. In the literature the convolutional distribution function is then examined and certain values of a specific, less general equivalent circuit model are calculated from which aspects of the original chemical processes are derived. We attempted to instead directly determine the original DRT from the calculated convolutional distribution function. This method proved to be practically less useful due to certain values determined at the time of experiment which meant the original DRT could only be recovered in a window which would not normally contain the desired information for the original DRT. This limits any attempt to extend the solution for the convolutional distribution function to the original DRT. Further research may determine a method for interpreting the convolutional distribution function without an equivalent circuit model as is done with the regularization method used to solve directly for the original DRT.
ContributorsBaker, Robert Simpson (Author) / Renaut, Rosemary (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Deconvolution of noisy data is an ill-posed problem, and requires some form of regularization to stabilize its solution. Tikhonov regularization is the most common method used, but it depends on the choice of a regularization parameter λ which must generally be estimated using one of several common methods. These methods can be computationally intensive, so I consider their behavior when only a portion of the sampled data is used. I show that the results of these methods converge as the sampling resolution increases, and use this to suggest a method of downsampling to estimate λ. I then present numerical results showing that this method can be feasible, and propose future avenues of inquiry.
ContributorsHansen, Jakob Kristian (Author) / Renaut, Rosemary (Thesis director) / Cochran, Douglas (Committee member) / Barrett, The Honors College (Contributor) / School of Music (Contributor) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
The solution of the linear system of equations $Ax\approx b$ arising from the discretization of an ill-posed integral equation with a square integrable kernel is considered. The solution by means of Tikhonov regularization in which $x$ is found to as the minimizer of $J(x)=\{ \|Ax -b\|_2^2 + \lambda^2 \|L x\|_2^2\}$ introduces the unknown regularization parameter $\lambda$ which trades off the fidelity of the solution data fit and its smoothing norm, which is determined by the choice of $L$. The Generalized Discrepancy Principle (GDP) and Unbiased Predictive Risk Estimator (UPRE) are methods for finding $\lambda$ given prior conditions on the noise in the measurements $b$. Here we consider the case of $L=I$, and hence use the relationship between the singular value expansion and the singular value decomposition for square integrable kernels to prove that the GDP and UPRE estimates yield a convergent sequence for $\lambda$ with increasing problem size. Hence the estimate of $\lambda$ for a large problem may be found by down-sampling to a smaller problem, or to a set of smaller problems, and applying these estimators more efficiently on the smaller problems. In consequence the large scale problem can be solved in a single step immediately with the parameter found from the down sampled problem(s).
ContributorsHorst, Michael Jacob (Author) / Renaut, Rosemary (Thesis director) / Cochran, Douglas (Committee member) / Wang, Yang (Committee member) / Barrett, The Honors College (Contributor) / School of Music (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
Description
Multiple-channel detection is considered in the context of a sensor network where data can be exchanged directly between sensor nodes that share a common edge in the network graph. Optimal statistical tests used for signal source detection with multiple noisy sensors, such as the Generalized Coherence (GC) estimate, use pairwise measurements from every pair of sensors in the network and are thus only applicable when the network graph is completely connected, or when data are accumulated at a common fusion center. This thesis presents and exploits a new method that uses maximum-entropy techniques to estimate measurements between pairs of sensors that are not in direct communication, thereby enabling the use of the GC estimate in incompletely connected sensor networks. The research in this thesis culminates in a main conjecture supported by statistical tests regarding the topology of the incomplete network graphs.
ContributorsCrider, Lauren Nicole (Author) / Cochran, Douglas (Thesis director) / Renaut, Rosemary (Committee member) / Kosut, Oliver (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
Description
Divergence-free vector field interpolants properties are explored on uniform and scattered nodes, and also their application to fluid flow problems. These interpolants may be applied to physical problems that require the approximant to have zero divergence, such as the velocity field in the incompressible Navier-Stokes equations and the magnetic and electric fields in the Maxwell's equations. In addition, the methods studied here are meshfree, and are suitable for problems defined on complex domains, where mesh generation is computationally expensive or inaccurate, or for problems where the data is only available at scattered locations.
The contributions of this work include a detailed comparison between standard and divergence-free radial basis approximations, a study of the Lebesgue constants for divergence-free approximations and their dependence on node placement, and an investigation of the flat limit of divergence-free interpolants. Finally, numerical solvers for the incompressible Navier-Stokes equations in primitive variables are implemented using discretizations based on traditional and divergence-free kernels. The numerical results are compared to reference solutions obtained with a spectral
method.
The contributions of this work include a detailed comparison between standard and divergence-free radial basis approximations, a study of the Lebesgue constants for divergence-free approximations and their dependence on node placement, and an investigation of the flat limit of divergence-free interpolants. Finally, numerical solvers for the incompressible Navier-Stokes equations in primitive variables are implemented using discretizations based on traditional and divergence-free kernels. The numerical results are compared to reference solutions obtained with a spectral
method.
ContributorsAraujo Mitrano, Arthur (Author) / Platte, Rodrigo (Thesis advisor) / Wright, Grady (Committee member) / Welfert, Bruno (Committee member) / Gelb, Anne (Committee member) / Renaut, Rosemary (Committee member) / Arizona State University (Publisher)
Created2016
Description
Solving partial differential equations on surfaces has many applications including modeling chemical diffusion, pattern formation, geophysics and texture mapping. This dissertation presents two techniques for solving time dependent partial differential equations on various surfaces using the partition of unity method. A novel spectral cubed sphere method that utilizes the windowed Fourier technique is presented and used for both approximating functions on spherical domains and solving partial differential equations. The spectral cubed sphere method is applied to solve the transport equation as well as the diffusion equation on the unit sphere. The second approach is a partition of unity method with local radial basis function approximations. This technique is also used to explore the effect of the node distribution as it is well known that node choice plays an important role in the accuracy and stability of an approximation. A greedy algorithm is implemented to generate good interpolation nodes using the column pivoting QR factorization. The partition of unity radial basis function method is applied to solve the diffusion equation on the sphere as well as a system of reaction-diffusion equations on multiple surfaces including the surface of a red blood cell, a torus, and the Stanford bunny. Accuracy and stability of both methods are investigated.
ContributorsIslas, Genesis Juneiva (Author) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Espanol, Malena (Committee member) / Kao, Ming-Hung (Committee member) / Renaut, Rosemary (Committee member) / Arizona State University (Publisher)
Created2021
Description
This thesis addresses the problem of approximating analytic functions over general and compact multidimensional domains. Although the methods we explore can be used in complex domains, most of the tests are performed on the interval $[-1,1]$ and the square $[-1,1]\times[-1,1]$. Using Fourier and polynomial frame approximations on an extended domain, well-conditioned methods can be formulated. In particular, these methods provide exponential decay of the error down to a finite but user-controlled tolerance $\epsilon>0$. Additionally, this thesis explores two implementations of the frame approximation: a singular value decomposition (SVD)-regularized least-squares fit as described by Adcock and Shadrin in 2022, and a column and row selection method that leverages QR factorizations to reduce the data needed in the approximation. Moreover, strategies to reduce the complexity of the approximation problem by exploiting randomized linear algebra in low-rank algorithms are also explored, including the AZ algorithm described by Coppe and Huybrechs in 2020.
ContributorsGuo, Maosheng (Author) / Platte, Rodrigo (Thesis advisor) / Espanol, Malena (Committee member) / Renaut, Rosemary (Committee member) / Arizona State University (Publisher)
Created2023