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- Fourier series (2)
- Gegenbauer polynomials (2)
- Gibbs phenomenon (2)
- Inverse polynomial reconstruction (2)
- Jacobi polynomials (2)
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- Laguerre polynomials (2)
- Probability of a biconditional (2)
- Probability of a conditional (2)
- Aluthge transform (1)
- Bayes' theorem (1)
- Error analysis (1)
- Gegenbauer reconstruction (1)
- Hermite polynomials (1)
- Hermite polynomials. (1)
- Inverse wavelet reconstruction (1)
- Polar decomposition (1)
- Probability of a material implication (1)
- Probability of an implication (1)
- Similarity orbit (1)
- Stable manifold theorem (1)
- Wavelets (1)
Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Methods Of Assessing And Ranking Probable Sources Of Error, Nataniel Greene
Methods Of Assessing And Ranking Probable Sources Of Error, Nataniel Greene
Publications and Research
A classical method for ranking n potential events as sources of error is Bayes' theorem. However, a ranking based on Bayes' theorem lacks a fundamental symmetry: the ranking in terms of blame for error will not be the reverse of the ranking in terms of credit for lack of error. While this is not a flaw in Bayes' theorem, it does lead one to inquire whether there are related methods which have such symmetry. Related methods explored here include the logical version of Bayes' theorem based on probabilities of conditionals, probabilities of biconditionals, and ratios or differences of credit to …
A Wavelet-Based Method For Overcoming The Gibbs Phenomenon, Nataniel Greene
A Wavelet-Based Method For Overcoming The Gibbs Phenomenon, Nataniel Greene
Publications and Research
The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the discontinuities. Here we describe a numerical procedure for overcoming the Gibbs phenomenon called the inverse wavelet reconstruction method. The method takes the Fourier coefficients of an oscillatory partial sum and uses them to construct the wavelet coefficients of a non-oscillatory wavelet series.
An Overview Of Conditionals And Biconditionals In Probability, Nataniel Greene
An Overview Of Conditionals And Biconditionals In Probability, Nataniel Greene
Publications and Research
Conditional and biconditional statements are a standard part of symbolic logic but they have only recently begun to be explored in probability for applications in artificial intelligence. Here we give a brief overview of the major theorems involved and illustrate them using two standard model problems from conditional probability.
Fourier Series Of Orthogonal Polynomials, Nataniel Greene
Fourier Series Of Orthogonal Polynomials, Nataniel Greene
Publications and Research
Explicit formulas for the Fourier coefficients of the Legendre polynomials can be found in the Bateman Manuscript Project. However, similar formulas for more general classes of orthogonal polynomials do not appear to have been worked out. Here we derive explicit formulas for the Fourier series of Gegenbauer, Jacobi, Laguerre and Hermite polynomials.
Formulas For The Fourier Series Of Orthogonal Polynomials In Terms Of Special Functions, Nataniel Greene
Formulas For The Fourier Series Of Orthogonal Polynomials In Terms Of Special Functions, Nataniel Greene
Publications and Research
An explicit formula for the Fourier coefficient of the Legendre polynomials can be found in the Bateman Manuscript Project. However, formulas for more general classes of orthogonal polynomials do not appear to have been worked out. Here we derive explicit formulas for the Fourier series of Gegenbauer, Jacobi, Laguerre and Hermite polynomials. The methods described here apply in principle to a class of polynomials, including non-orthogonal polynomials.
Inverse Wavelet Reconstruction For Resolving The Gibbs Phenomenon, Nataniel Greene
Inverse Wavelet Reconstruction For Resolving The Gibbs Phenomenon, Nataniel Greene
Publications and Research
The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the discontinuities. Here we describe a numerical procedure for overcoming the Gibbs phenomenon called the inverse wavelet reconstruction method. The method takes the Fourier coefficients of an oscillatory partial sum and uses them to construct the wavelet coefficients of a non-oscillatory wavelet series.
Iterated Aluthge Transforms: A Brief Survey, Jorge Antezana, Enrique R. Pujals, Demetrio Stojanoff
Iterated Aluthge Transforms: A Brief Survey, Jorge Antezana, Enrique R. Pujals, Demetrio Stojanoff
Publications and Research
Given an r × r complex matrix T, if T = U|T| is the polar decomposition of T, then the Aluthge transform is defined by
∆(T) = |T|1/2U|T|1/2.
Let ∆n(T) denote the n-times iterated Aluthge transform of T, i.e. ∆0(T) = T and ∆n(T) = ∆(∆n−1(T)), n ∈ N. In this paper we make a brief survey on the known properties and applications of …