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Showing 1 to 20 of 54 for “"orthogonal polynomials"”.
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Multivariate orthogonal polynomials
The object of this thesis is to define special orthogonal polynomials and develop efficient methods for employing them which have the same advantages with respect to functions of the type (1.2) as do univariate orthogonal polynomials in the simple case k=1. These new polynomials may be usefully …
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Time-series analysis using orthogonal polynomials
Advances in the study of non-linear dynamics have encouraged the construction of models and simulators of non-linear time-series. Researchers in the field of both science and statistics have come up with innovative methods that are useful in extracting information from systems that exhibit …
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Matrix valued orthogonal polynomials and quantum groups
Contains fulltext : 150268.pdf (Publisher’s version ) (Open Access)
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Isospectral algorithms, Toeplitz matrices and orthogonal polynomials
… in some fashion, and one directly involving orthogonal polynomials. The first set of algorithms we study come from discretising a continuous isospectral flow designed to converge to a symmetric Toeplitz matrix with prescribed eigenvalues. We analyse constrained, isospectral gradient flow …
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Discrete Harmonic Analysis related to classical orthogonal polynomials
… to the one associated with classical orthogonal polynomials. Its aim is the study of the discrete analogues of some classical operators in Harmonic Analysis. To be specific, the convergence problem of the multiplier of an interval for discrete Fourier series and the problem of the norm …
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On orthogonal polynomials and related discrete integrable systems
Orthogonal polynomials arise in many areas of mathematics and have been the subject of interest by many mathematicians. In recent years this interest has often arisen from outside the orthogonal polynomial community after their connection with integrable systems was found. This thesis is concerned …
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Method of Orthogonal Polynomials in Plane Theory of Elasticity
Made available in DSpace on 2014-12-10T17:25:43Z (GMT). No. of bitstreams: 1 6808219.pdf: 967413 bytes, checksum: e804ac93c419eefa8790b7c2e80404a1 (MD5) Previous issue date: 1967
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Flexural-Torsional Coupled Vibration of Rotating Beams Using Orthogonal Polynomials
… beams using the Rayleigh-Ritz method with orthogonal polynomials as basis functions is studied. The present work starts from a review of the development and analysis of four basic types of beam theories: the Euler-Bernoulli, Rayleigh, Shear and Timoshenko and goes over to a study of …
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Poncelet polygons through the lenses of orthogonal polynomials on the unit circle, finite Blaschke products, and numerical ranges.
… product. The other involves the zero sets of paraorthogonal polynomials on the unit circle. In all three cases, the intersection of the polygons in this family forms part of an algebraic curve, which will be the primary focus of our study. A large part of this dissertation is dedicated to making …
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Orthogonal Polynomials On An Arc Of The Unit Circle With Respect To A Generalized Jacobi Weight: A Riemann-Hilbert Method Approach
We investigate the asymptotic behavior of polynomials orthogonal over a symmetric arc of the unit circle with respect to a generalized Jacobi-type weight. Full asymptotic expansions for the orthogonal polynomials are obtained at every point of the complex plane. Our method of proof is based on a …
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Exact Solutions to the Six-Vertex Model with Domain Wall Boundary Conditions and Uniform Asymptotics of Discrete Orthogonal Polynomials on an Infinite Lattice
… $n$ asymptotics for a corresponding system of orthogonal polynomials. To deal with this problem in the antiferroelectric phase region, we consequently develop an asymptotic analysis, based on a Riemann-Hilbert approach, for orthogonal polynomials on an infinite regular lattice with respect to …
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Orthogonal matrix polynomials and differential, difference and q-difference matrix operators
… result that are framed in the theory of Matrix Orthogonal Polynomials, a branch of the very celebrated subject of Orthogonal Polynomials. In particular we study families of matrix valued orthogonal polynomials satisfying differential, difference or q-difference equations. The search for examples …
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Option pricing in a path integral framework
… the option value at each time step. The Hermite orthogonal polynomials and their associated properties are employed to create a set of recurrence relations so that a final option pricing polynomial is formed. A similar approach using normalised Hermite orthogonal polynomials is also presented. …
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Image feature matching using polynomial representation of chain codes
… descriptor is based on a truncated series of orthogonal polynomials used to represent a piecewise continuous function derived from a chain code. This piecewise continuous function is generated from a chain code by mapping individual chain links onto real numbers. A variety of alternative …
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Rodrigues Formula for Jacobi Polynomials on the Unit Circle
We begin by discussing properties of orthogonal polynomials on a Borel measurable subset of the complex plane. Then we focus on Jacobi polynomials and give a formula (analogous to the one discovered by R. D. Costin) for finding Jacobi polynomials on the unit circle. Finally, we consider some …
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An Introduction To Hellmann-feynman Theory
… the variation of zeros of special functions and orthogonal polynomials are surveyed. Possible extensions are discussed.
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Analyses of the Lanczos Algorithm and of the Approximation Problem in Richardson's Method
… solved by the algorithm. An investigation of the orthogonal polynomials associated with the algorithm partially explains the observed phenomena.
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