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- Long memory (2)
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Articles 1 - 12 of 12
Full-Text Articles in Physical Sciences and Mathematics
Stability And Error Estimates For Vector Field Interpolation And Decomposition On The Sphere With Rbfs, Edward J. Fuselier, Grady Wright
Stability And Error Estimates For Vector Field Interpolation And Decomposition On The Sphere With Rbfs, Edward J. Fuselier, Grady Wright
Mathematics Faculty Publications and Presentations
A new numerical technique based on radial basis functions (RBFs) is presented for fitting a vector field tangent to the sphere, S2, from samples of the field at "scattered" locations on S2. The method naturally provides a way to decompose the reconstructed field into its individual Helmholtz–Hodge components, i.e., into divergence-free and curl-free parts, which is useful in many applications from the atmospheric and oceanic sciences (e.g., in diagnosing the horizontal wind and ocean currents). Several approximation results for the method will be derived. In particular, Sobolevtype error estimates are obtained for both the interpolant and …
Wavelet-Based Bayesian Estimation Of Partially Linear Regression Models With Long Memory Errors, Kyungduk Ko, Leming Qu, Marina Vannucci
Wavelet-Based Bayesian Estimation Of Partially Linear Regression Models With Long Memory Errors, Kyungduk Ko, Leming Qu, Marina Vannucci
Mathematics Faculty Publications and Presentations
In this paper we focus on partially linear regression models with long memory errors, and propose a wavelet-based Bayesian procedure that allows the simultaneous estimation of the model parameters and the nonparametric part of the model. Employing discrete wavelet transforms is crucial in order to simplify the dense variance-covariance matrix of the long memory error. We achieve a fully Bayesian inference by adopting a Metropolis algorithm within a Gibbs sampler. We evaluate the performances of the proposed method on simulated data. In addition, we present an application to Northern hemisphere temperature data, a benchmark in the long memory literature.
Error And Stability Estimates For Surface-Divergence Free Rbf Interpolants On The Sphere, Edward J. Fuselier, Francis J. Narcowich, Joseph D. Ward, Grady Wright
Error And Stability Estimates For Surface-Divergence Free Rbf Interpolants On The Sphere, Edward J. Fuselier, Francis J. Narcowich, Joseph D. Ward, Grady Wright
Mathematics Faculty Publications and Presentations
Recently, a new class of surface-divergence free radial basis function interpolants has been developed for surfaces in R3. In this paper, several approximation results for this class of interpolants will be derived in the case of the sphere, S2. In particular, Sobolev-type error estimates are obtained, as well as optimal stability estimates for the associated interpolation matrices. In addition, a Bernstein estimate and an inverse theorem are also derived. Numerical validation of the theoretical results is also given.
Solvability Characterizations Of Pell Like Equations, Jason Smith
Solvability Characterizations Of Pell Like Equations, Jason Smith
Boise State University Theses and Dissertations
Pell's equation has intrigued mathematicians for centuries. First stated as Archimedes' Cattle Problem, Pell's equation, in its most general form, X2 – P • Y2 = 1, where P is any square free positive integer and solutions are pairs of integers, has seen many approaches but few general solutions. The eleventh century Indian mathematician Bhaskara solved X2 – 61 • Y2 = 1 and, in response to Fermat's challenge, Wallis and Brouncker gave solutions to X2 – 151 • Y2 = 1 and X2 –313 • Y2 = 1. Fermat claimed to …
Transparency In Formal Proof, Cap Petschulat
Transparency In Formal Proof, Cap Petschulat
Boise State University Theses and Dissertations
The oft-emphasized virtue of formal proof is correctness; a machine-checked proof adds greatly to our confidence in a result. But the rigors of formalization give rise to another possible virtue, namely clarity. Given the state of the art, clarity and formality are at odds: complexity of formalization obscures the content of proof. To address this, we develop a notion of proof strategies which extend the well-known notion of proof tactics. Beginning with the foundations of logic, we describe the methods and structures necessary to implement proof strategies, concluding with a proof-of-concept implementation in CheQED, a web-based proof assistant.
Discrete Variable Methods For Delay-Differential Equations With Threshold-Type Delays, Z. Jackiewicz, Barbara Zubik-Kowal
Discrete Variable Methods For Delay-Differential Equations With Threshold-Type Delays, Z. Jackiewicz, Barbara Zubik-Kowal
Mathematics Faculty Publications and Presentations
We study numerical solution of systems of delay-differential equations in which the delay function, which depends on the unknown solution, is defined implicitly by the threshold condition. We study discrete variable numerical methods for these problems and present error analysis. The global error is composed of the error of solving the differential systems, the error from the threshold conditions and the errors in delay arguments. Our theoretical analysis is confirmed by numerical experiments on threshold problems from the theory of epidemics and from population dynamics.
Finite-Difference And Pseudo-Sprectral Methods For The Numerical Simulations Of In Vitro Human Tumor Cell Population Kinetics, Z. Jackiewicz, Barbara Zubik-Kowal, B. Basse
Finite-Difference And Pseudo-Sprectral Methods For The Numerical Simulations Of In Vitro Human Tumor Cell Population Kinetics, Z. Jackiewicz, Barbara Zubik-Kowal, B. Basse
Mathematics Faculty Publications and Presentations
Pseudo-spectral approximations are constructed for the model equations which describe the population kinetics of human tumor cells in vitro and their responses to radiotherapy or chemotherapy. These approximations are more efficient than finite-difference approximations. The spectral accuracy of the pseudo-spectral method allows us to resolve the model with a much smaller number of spatial grid-points than required for the finite-difference method to achieve comparable accuracy. This is demonstrated by numerical experiments which show a good agreement between predicted and experimental data.
A Radial Basis Function Method For The Shallow Water Equations On A Sphere, Natasha Flyer, Grady Wright
A Radial Basis Function Method For The Shallow Water Equations On A Sphere, Natasha Flyer, Grady Wright
Mathematics Faculty Publications and Presentations
The paper derives the first known numerical shallow water model on the sphere using radial basis function (RBF) spatial discretisation, a novel numerical methodology that does not require any grid or mesh. In order to perform a study with regard to its spatial and temporal errors, two nonlinear test cases with known analytical solutions are considered. The first is global steady-state flow with a compactly supported velocity field while the second is unsteady flow where features in the flow must be kept intact without dis- persion. This behavior is achieved by introducing forcing terms in the shallow water equations. Error …
Proportional Reasoning 101, Laurie O. Cavey
First-Order Bias Correction For Fractionally Integrated Time Series, Jaechoul Lee, Kyungduk Ko
First-Order Bias Correction For Fractionally Integrated Time Series, Jaechoul Lee, Kyungduk Ko
Mathematics Faculty Publications and Presentations
Most of the long memory estimators for stationary fractionally integrated time series models are known to experience non-negligible bias in small and finite samples. Simple moment estimators are also vulnerable to such bias, but can easily be corrected. In this paper, we propose bias reduction methods for a lag-one sample autocorrelation-based moment estimator. In order to reduce the bias of the moment estimator, we explicitly obtain the exact bias of lag-one sample autocorrelation up to the order n−1. An example where the exact first-order bias can be noticeably more accurate than its asymptotic counterpart, even for large samples, is presented. …
Wavelet Reconstruction Of Nonuniformly Sampled Signals, Leming Qu, Partha S. Routh, Phil D. Anno
Wavelet Reconstruction Of Nonuniformly Sampled Signals, Leming Qu, Partha S. Routh, Phil D. Anno
Mathematics Faculty Publications and Presentations
For the reconstruction of a nonuniformly sampled signal based on its noisy observations, we propose a level dependent l1 penalized wavelet reconstruction method. The LARS/Lasso algorithm is applied to solve the Lasso problem. The data adaptive choice of the regularization parameters is based on the AIC and the degrees of freedom is estimated by the number of nonzero elements in the Lasso solution. Simulation results conducted on some commonly used 1_D test signals illustrate that the proposed method possesses good empirical properties.
A Newton Root-Finding Algorithm For Estimating The Regularization Parameter For Solving Ill-Conditioned Least Squares Problems, Jodi Mead, Rosemary Renaut
A Newton Root-Finding Algorithm For Estimating The Regularization Parameter For Solving Ill-Conditioned Least Squares Problems, Jodi Mead, Rosemary Renaut
Mathematics Faculty Publications and Presentations
We discuss the solution of numerically ill-posed overdetermined systems of equations using Tikhonov a-priori-based regularization. When the noise distribution on the measured data is available to appropriately weight the fidelity term, and the regularization is assumed to be weighted by inverse covariance information on the model parameters, the underlying cost functional becomes a random variable that follows a X2 distribution. The regularization parameter can then be found so that the optimal cost functional has this property. Under this premise a scalar Newton root-finding algorithm for obtaining the regularization parameter is presented. The algorithm, which uses the singular value …