# Numerical Analysis and Computation Commons™

## All Articles in Numerical Analysis and Computation

841 full-text articles. Page 1 of 29.

On The Interval Generalized Coupled Matrix Equations, 2019 Shahid Chamran University of Ahvaz

#### On The Interval Generalized Coupled Matrix Equations, Marzieh Dehghani-Madiseh

##### Electronic Journal of Linear Algebra

In this work, the interval generalized coupled matrix equations \begin{equation*} \sum_{j=1}^{p}{{\bf{A}}_{ij}X_{j}}+\sum_{k=1}^{q}{Y_{k}{\bf{B}}_{ik}}={\bf{C}}_{i}, \qquad i=1,\ldots,p+q, \end{equation*} are studied in which ${\bf{A}}_{ij}$, ${\bf{B}}_{ik}$ and ${\bf{C}}_{i}$ are known real interval matrices, while $X_{j}$ and $Y_{k}$ are the unknown matrices for $j=1,\ldots,p$, $k=1,\ldots,q$ and $i=1,\ldots,p+q$. This paper discusses the so-called AE-solution sets for this system ...

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, 2018 Wojciech Budzianowski Consulting Services

#### Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

##### Wojciech Budzianowski

No abstract provided.

Determinantal Properties Of Generalized Circulant Hadamard Matrices, 2018 National and Kapodistrian University of Athens

#### Determinantal Properties Of Generalized Circulant Hadamard Matrices, Marilena Mitrouli, Ondrej Turek

##### Electronic Journal of Linear Algebra

The derivation of analytical formulas for the determinant and the minors of a given matrix is in general a difficult and challenging problem. The present work is focused on calculating minors of generalized circulant Hadamard matrices. The determinantal properties are studied explicitly, and generic theorems specifying the values of all the minors for this class of matrices are derived. An application of the derived formulae to an interesting problem of numerical analysis, the growth problem, is also presented.

2018 Athens University of Economics and Business

#### Asymptotic Results On The Condition Number Of Fd Matrices Approximating Semi-Elliptic Pdes, Paris Vassalos

##### Electronic Journal of Linear Algebra

This work studies the asymptotic behavior of the spectral condition number of the matrices $A_{nn}$ arising from the discretization of semi-elliptic partial differential equations of the form \bdm -\left( a(x,y)u_{xx}+b(x,y)u_{yy}\right)=f(x,y), \edm on the square $\Omega=(0,1)^2,$ with Dirichlet boundary conditions, where the smooth enough variable coefficients $a(x,y), b(x,y)$ are nonnegative functions on $\overline{\Omega}$ with zeros. In the case of coefficient functions with a single and common zero, it is discovered that apart from the minimum order of the zero ...

2018 Utah State University

#### Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg

##### All Graduate Plan B and other Reports

Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms ...

#### Stochastic Lanczos Likelihood Estimation Of Genomic Variance Components, Richard Border

##### Applied Mathematics Graduate Theses & Dissertations

Genomic variance components analysis seeks to estimate the extent to which interindividual variation in a given trait can be attributed to genetic similarity. Likelihood estimation of such models involves computationally expensive operations on large, dense, and unstructured matrices of high rank. As a result, standard estimation procedures relying on direct matrix methods become prohibitively expensive as sample sizes increase. We propose a novel estimation procedure that uses the Lanczos process and stochastic Lanczos quadrature to approximate the likelihood for an initial choice of parameter values. Then, by identifying the variance components parameter space with a family of shifted linear systems ...

Structured Eigenvalue/Eigenvector Backward Errors Of Matrix Pencils Arising In Optimal Control, 2018 Technische Universitaet Berlin

#### Structured Eigenvalue/Eigenvector Backward Errors Of Matrix Pencils Arising In Optimal Control, Christian Mehl, Volker Mehrmann, Punit Sharma

##### Electronic Journal of Linear Algebra

Eigenvalue and eigenpair backward errors are computed for matrix pencils arising in optimal control. In particular, formulas for backward errors are developed that are obtained under block-structure-preserving and symmetry-structure-preserving perturbations. It is shown that these eigenvalue and eigenpair backward errors are sometimes significantly larger than the corresponding backward errors that are obtained under perturbations that ignore the special structure of the pencil.

Convergence Of A Modified Newton Method For A Matrix Polynomial Equation Arising In Stochastic Problem, 2018 Pusan National University

#### Convergence Of A Modified Newton Method For A Matrix Polynomial Equation Arising In Stochastic Problem, Sang-Hyup Seo Mr., Jong-Hyeon Seo Dr., Hyun-Min Kim Prof.

##### Electronic Journal of Linear Algebra

The Newton iteration is considered for a matrix polynomial equation which arises in stochastic problem. In this paper, it is shown that the elementwise minimal nonnegative solution of the matrix polynomial equation can be obtained using Newton's method if the equation satisfies the sufficient condition, and the convergence rate of the iteration is quadratic if the solution is simple. Moreover, it is shown that the convergence rate is at least linear if the solution is non-simple, but a modified Newton method whose iteration number is less than the pure Newton iteration number can be applied. Finally, numerical experiments are ...

2018 University of New Mexico

#### Two Applications Of High Order Methods: Wave Propagation And Accelerator Physics, Oleksii Beznosov

##### Shared Knowledge Conference

Numerical simulations of partial differential equations (PDE) are used to predict the behavior of complex physics phenomena when the real life experiments are expensive. Discretization of a PDE is the representation of the continuous problem as a discrete problem that can be solved on a computer. The discretization always introduces a certain inaccuracy caused by the numerical approximation. By increasing the computational cost of the numerical algorithm the solution can be computed more accurately. In the theory of numerical analysis this fact is called the convergence of the numerical algorithm. The idea behind high order methods is to improve the ...

Estimators Comparison Of Separable Covariance Structure With One Component As Compound Symmetry Matrix, 2018 Poznan University of Technology

#### Estimators Comparison Of Separable Covariance Structure With One Component As Compound Symmetry Matrix, Katarzyna Filipiak, Daniel Klein, Monika Mokrzycka

##### Electronic Journal of Linear Algebra

The maximum likelihood estimation (MLE) of separable covariance structure with one component as compound symmetry matrix has been widely studied in the literature. Nevertheless, the proposed estimates are not given in explicit form and can be determined only numerically. In this paper we give an alternative form of MLE and we show that this new algorithm is much quicker than the algorithms given in the literature.\\ Another estimator of covariance structure can be found by minimizing the entropy loss function. In this paper we give three methods of finding the best approximation of separable covariance structure with one component as ...

On Projection Of A Positive Definite Matrix On A Cone Of Nonnegative Definite Toeplitz Matrices, 2018 Poznań University Of Technology

#### On Projection Of A Positive Definite Matrix On A Cone Of Nonnegative Definite Toeplitz Matrices, Katarzyna Filipiak, Augustyn Markiewicz, Adam Mieldzioc, Aneta Sawikowska

##### Electronic Journal of Linear Algebra

We consider approximation of a given positive definite matrix by nonnegative definite banded Toeplitz matrices. We show that the projection on linear space of Toeplitz matrices does not always preserve nonnegative definiteness. Therefore we characterize a convex cone of nonnegative definite banded Toeplitz matrices which depends on the matrix dimensions, and we show that the condition of positive definiteness given by Parter [{\em Numer. Math. 4}, 293--295, 1962] characterizes the asymptotic cone. In this paper we give methodology and numerical algorithm of the projection basing on the properties of a cone of nonnegative definite Toeplitz matrices. This problem can be ...

Positive And Z-Operators On Closed Convex Cones, 2018 University of Maryland Baltimore County

#### Positive And Z-Operators On Closed Convex Cones, Michael J. Orlitzky

##### Electronic Journal of Linear Algebra

Let $K$ be a closed convex cone with dual $\dual{K}$ in a finite-dimensional real Hilbert space. A \emph{positive operator} on $K$ is a linear operator $L$ such that $L\of{K} \subseteq K$. Positive operators generalize the nonnegative matrices and are essential to the Perron-Frobenius theory. It is said that $L$ is a \emph{\textbf{Z}-operator} on $K$ if % \begin{equation*} \ip{L\of{x}}{s} \le 0 \;\text{ for all } \pair{x}{s} \in \cartprod{K}{\dual{K}} \text{ such that } \ip{x}{s} = 0. \end{equation*} % The \textbf{Z}-operators are generalizations of \textbf{Z ...

2018 Illinois State University

#### Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

2018 Loyola Marymount University

#### Using Pair Approximation Methods To Analyze Behavior Of A Probabilistic Cellular Automaton Model For Intracellular Cardiac Calcium Dynamics, Robert J. Rovetti

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Issues In Reproducible Simulation Research, 2018 Loyola Marymount University

#### Issues In Reproducible Simulation Research, Ben G. Fitzpatrick

##### Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.

Boundary Homogenization And Capture Time Distributions Of Semipermeable Membranes With Periodic Patterns Of Reactive Sites, 2018 Harvey Mudd College

#### Boundary Homogenization And Capture Time Distributions Of Semipermeable Membranes With Periodic Patterns Of Reactive Sites, Andrew J. Bernoff, Daniel Schmidt, Alan E. Lindsay

##### All HMC Faculty Publications and Research

We consider the capture dynamics of a particle undergoing a random walk in a half- space bounded by a plane with a periodic pattern of absorbing pores. In particular, we numerically measure and asymptotically characterize the distribution of capture times. Numerically we develop a kinetic Monte Carlo (KMC) method that exploits exact solutions to create an efficient particle- based simulation of the capture time that deals with the infinite half-space exactly and has a run time that is independent of how far from the pores one begins. Past researchers have proposed homogenizing the surface boundary conditions, replacing the reflecting (Neumann ...

Investigation Of Chaos In Biological Systems, 2018 The University of Western Ontario

#### Investigation Of Chaos In Biological Systems, Navaneeth Mohan

##### Electronic Thesis and Dissertation Repository

Chaos is the seemingly irregular behavior arising from a deterministic system. Chaos is observed in many real-world systems. Edward Lorenz’s seminal discovery of chaotic behavior in a weather model has prompted researchers to develop tools that distinguish chaos from non-chaotic behavior. In the first chapter of this thesis, I survey the tools for detecting chaos namely, Poincaré maps, Lyapunov exponents, surrogate data analysis, recurrence plots and correlation integral plots. In chapter two, I investigate blood pressure fluctuations for chaotic signatures. Though my analysis reveals interesting evidence in support of chaos, the utility such an analysis lies in a different ...

Yelp’S Review Filtering Algorithm, 2018 Southern Methodist University

#### Yelp’S Review Filtering Algorithm, Yao Yao, Ivelin Angelov, Jack Rasmus-Vorrath, Mooyoung Lee, Daniel W. Engels

##### SMU Data Science Review

In this paper, we present an analysis of features influencing Yelp's proprietary review filtering algorithm. Classifying or misclassifying reviews as recommended or non-recommended affects average ratings, consumer decisions, and ultimately, business revenue. Our analysis involves systematically sampling and scraping Yelp restaurant reviews. Features are extracted from review metadata and engineered from metrics and scores generated using text classifiers and sentiment analysis. The coefficients of a multivariate logistic regression model were interpreted as quantifications of the relative importance of features in classifying reviews as recommended or non-recommended. The model classified review recommendations with an accuracy of 78%. We found that ...

2018 Air Force Institute of Technology

#### Statistical Inference To Evaluate And Compare The Performance Of Correlated Multi-State Classification Systems, Beau A. Nunnally

##### Theses and Dissertations

The current emphasis on including correlation when comparing diagnostic test performance is quite important, however, there are cases in which correlation effects may be negligible with respect to inference. This proposed work examines the impact of including correlation between classification systems with continuous features by comparing the optimal performance of two diagnostic tests with multiple outcomes as well as providing inference for a sequence of tests. We define the optimal point using Bayes Cost, a metric that sums the weighted misclassifications within a diagnostic test using a cost/benefit structure. Through simulation, we quantify the impact of correlation on standard ...

2018 University of Nebraska - Lincoln

#### On The Well-Posedness And Global Boundary Controllability Of A Nonlinear Beam Model, Jessie Jamieson

##### Dissertations, Theses, and Student Research Papers in Mathematics

The theory of beams and plates has been long established due to works spanning many fields, and has been explored through many investigations of beam and plate mechanics, controls, stability, and the well-posedness of systems of equations governing the motions of plates and beams. Additionally, recent investigations of flutter phenomena by Dowell, Webster et al. have reignited interest into the mechanics and stability of nonlinear beams. In this thesis, we wish to revisit the seminal well-posedness results of Lagnese and Leugering for the one dimensional, nonlinear beam from their 1991 paper, "Uniform stabilization of a nonlinear beam by nonlinear boundary ...