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Page 7053 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
Summary: “The stability of transformations between Taylor and Hermite, and Bernstein and Hermite forms of polynomials are investigated.  ...  65DI7 65F35 Hermann, Thomas (H-AOS-GD; Budapest) On the stability of polynomial transformations between Taylor, Bernstein and Hermite forms.  ... 

Transformation of Chebyshev–Bernstein Polynomial Basis

Abedallah Rababah
2003 Computational Methods in Applied Mathematics  
In paper [4] , transformation matrices mapping the Legendre and Bernstein forms of a polynomial of degree n into each other are derived and examined.  ...  Chebyshev polynomials with the geometrical insight of the Bernstein form.  ...  Acknowledgement: The author wishes to thank the referee for useful comments.  ... 
doi:10.2478/cmam-2003-0038 fatcat:es5yniykqbeznmremzzku6vbxy

Equivalences for Linearizations of Matrix Polynomials [article]

Robert M. Corless, Leili Rafiee Sevyeri, B. David Saunders
2021 arXiv   pre-print
In this paper we show how to use algorithms for computing the Hermite Normal Form of a companion matrix for a scalar polynomial to direct the discovery of unimodular matrix polynomial cofactors E(z) and  ...  One useful standard method to compute eigenvalues of matrix polynomials P(z) ∈ℂ^n× n[z] of degree at most ℓ in z (denoted of grade ℓ, for short) is to first transform P(z) to an equivalent linear matrix  ...  RMC thanks Froilán Dopico for several very useful discussions on linearization, giving several references, and pointing out the difference between local linearization and linearization.  ... 
arXiv:2102.09726v1 fatcat:n6d3krco4zbijj3r6tjehfkt7i

Differentiation Matrices for Univariate Polynomials [article]

Amirhossein Amiraslani and Robert M. Corless and Madhusoodan Gunasingham
2018 arXiv   pre-print
We collect here elementary properties of differentiation matrices for univariate polynomials expressed in various bases, including orthogonal polynomial bases and non-degree-graded bases such as Bernstein  ...  bases and Lagrange \& Hermite interpolational bases.  ...  We consider taking n + 1 nodes τ j for 0 ≤ j ≤ n, which gives us 3(n + 1) pieces of data and thus a polynomial of degree at most 3n + 2. We then plot the error p(z) − 1 on this interval.  ... 
arXiv:1809.05769v1 fatcat:efihdlm3o5hzbbhx25vit6ygoa

The Bernstein polynomial basis: A centennial retrospective

Rida T. Farouki
2012 Computer Aided Geometric Design  
This survey provides a brief historical perspective on the evolution of the Bernstein polynomial basis, and a synopsis of the current state of associated algorithms and applications.  ...  One hundred years after the introduction of the Bernstein polynomial basis, we survey the historical development and current state of theory, algorithms, and applications associated with this remarkable  ...  The paper has been greatly improved by the efforts of the anonymous referees, through their diligent reading of and perceptive comments on an initial draft.  ... 
doi:10.1016/j.cagd.2012.03.001 fatcat:eiqucogpb5gh3lh5gnoj7p32cq

Hermite interpolation by Minkowski Pythagorean hodograph curves and medial axis transform approximation

Jiří Kosinka, Zbyněk Šír
2010 Computer Aided Geometric Design  
We show that for any data there exists a four-parameter system of interpolants and we identify the one which preserves symmetry and planarity of the input data and which has the optimal approximation degree  ...  The new algorithm is applied to an efficient approximation of segments of the medial axis transform of a planar domain leading to rational parameterizations of the offsets of the domain boundaries with  ...  Acknowledgment ZbyněkŠír was supported by the project MSM 0021620839 of the Czech Ministry of Education and by the project no. 201/08/0486 of the Czech Science Foundation.  ... 
doi:10.1016/j.cagd.2010.04.005 fatcat:wxd3zzuwj5dwrh3pfi67aneteu

A unified approach to evaluation algorithms for multivariate polynomials

Suresh K. Lodha, Ron Goldman
1997 Mathematics of Computation  
We present a unified framework for most of the known and a few new evaluation algorithms for multivariate polynomials expressed in a wide variety of bases including the Bernstein-Bézier, multinomial (or  ...  Taylor), Lagrange and Newton bases.  ...  Acknowledgments We wish to thank the anonymous referee whose comments helped us to improve the presentation of this work.  ... 
doi:10.1090/s0025-5718-97-00862-4 fatcat:37audtlqq5a4zkbodg6lmeyg64

Iterated Bernstein operators for distribution function and density estimation: Balancing between the number of iterations and the polynomial degree

Claude Manté
2015 Computational Statistics & Data Analysis  
An original method for estimating distribution functions and densities with Bernstein polynomials is proposed, which takes advantage of results about the eigenstructure of the Bernstein operator to refine  ...  Despite its slow convergence, the use of the Bernstein polynomial approximation is becoming more frequent in Statistics, especially for density estimation of compactly supported probability distributions  ...  Acknowledgements The author is very grateful to the referees for their numerous and helpful comments and suggestions, and to Starrlight Augustine for greatly improving the English text.  ... 
doi:10.1016/j.csda.2014.11.003 fatcat:pykutefghbb6voyzazdlk4fu2i

On edge detection

V Torre, T A Poggio
1986 IEEE Transactions on Software Engineering  
In particular, we characterize the relation between the Laplacian and the second directional derivative along the gradient.  ...  A critical, intermediate goal of edge detection is the detection and characterization of significant intensity changes. This paper discusses this part of the edge detection problem.  ...  Hildreth read the manuscript and provided tremendously useful and poorly implemented suggestions.  ... 
pmid:21869334 fatcat:oo7pqazxmjd7zoght7m6lbz7je

Smooth Parametric Surfaces and n-Sided Patches [chapter]

John A. Gregory, Vincent K. H. Lau, Jianwei Zhou
1990 Computation of Curves and Surfaces  
The theory of 'geometric continuity' within the subject of CAGD is reviewed.  ...  The theory is applied to the problem of filling an n-sided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed.  ...  Hahn, whose insight has greatly helped our own understanding of the subject of smooth parametric surfaces.  ... 
doi:10.1007/978-94-009-2017-0_14 fatcat:b4e5h7iiardw5bgrsqkyruyree

Theory of one-dimensional Vlasov-Maxwell equilibria: with applications to collisionless current sheets and flux tubes [article]

Oliver Allanson
2017 arXiv   pre-print
We develop the theory of inversion using expansions in Hermite polynomials of the canonical momenta.  ...  For large classes of DFs, we prove that non-negativity of the distribution function is contingent on the magnetisation of the plasma, and make conjectures for all classes.  ...  Fourier transform or Hermite polynomial expansion) has an effect on the outcome.  ... 
arXiv:1710.01348v1 fatcat:jbiwipsl5bfvrolgvhxj7kwfgy

A Blossoming Development of Splines

Stephen Mann
2006 Synthesis Lectures on Computer Graphics and Animation  
Bézier/B-splines represent polynomials and piecewise polynomials in a geometric manner using sets of control points that define the shape of the surface.  ...  In this lecture, we study Bézier and B-spline curves and surfaces, mathematical representations for free-form curves and surfaces that are common in CAD systems and are used to design aircraft and automobiles  ...  BERNSTEIN POLYNOMIALS AND BÉZIER CURVES A third polynomial basis that we will consider is the Bernstein basis, which is used to form Bézier curves.  ... 
doi:10.2200/s00041ed1v01200607cgr001 fatcat:5shteg26izdvdj4ndz2xb6xv2m

On the Le Cam distance between Poisson and Gaussian experiments and the asymptotic properties of Szasz estimators [article]

Frédéric Ouimet
2021 arXiv   pre-print
We then apply the result to derive an upper bound on the Le Cam distance between Poisson and Gaussian experiments, which gives a complete proof of the sketch provided in the unpublished set of lecture  ...  We also use the local limit theorem to derive the asymptotics of the variance for Bernstein c.d.f. and density estimators with Poisson weights on the positive half-line (also called Szasz estimators).  ...  Acknowledgments The author would like to thank an anonymous referee for his valuable comments that led to improvements in the presentation of this paper  ... 
arXiv:2010.05146v3 fatcat:j5rlusfzjzhg5lfmwadyn3shma

Brief on order-reduction for models: a critical survey

Nguyễn Thụy Anh, Nguyễn Ngọc San
2013 Journal of Computer Science and Cybernetics  
of the original modeled states.  ...  A critical comparison is made of the extent to which the models obtained from the optimal projection equations adopting state -optimization method proposed by authors are seen retaining the physical significance  ...  Acknow ledgment The authors are thankful to Dr. N. G. Nath, Professor of Radio-Physics and Electronics Dept. University of Calcutta for valuable discussion on the first draft of the paper in 1994.  ... 
doi:10.15625/1813-9663/16/1/2845 fatcat:xlbsetcjpjc4nn33eelujw4w6q

Stable Bayesian Optimisation via Direct Stability Quantification [article]

Alistair Shilton, Sunil Gupta, Santu Rana, Svetha Venkatesh, Majid Abdolshah, Dang Nguyen
2019 arXiv   pre-print
are then used to (a) guide the optimisation process toward solutions satisfying our stability criteria and (b) post-filter results to find the best stable solution.  ...  We exhibit our algorithm on synthetic and real-world problems and demonstrate that it is able to effectively find stable maxima.  ...  Throughout this section we use the shorthand: f (i) (x) = ∂ i ∂x i f (x) We will also be using the Hermite polynomials H q and the normalised Hermite polynomials (Hermite functions) h q [1] : H q (x)  ... 
arXiv:1902.07846v1 fatcat:bvhl5e5is5h7fgsod6zgbnk3be
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