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Polynomial spline spaces of non-uniform bi-degree on T-meshes: Combinatorial bounds on the dimension
[article]
2019
arXiv
pre-print
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The latter allows for the flexibility of choosing non-uniform bi-degrees for the splines, i.e., different bi-degrees on different faces of the T-mesh. ...
Focusing on T-meshes, we study the dimension of the space of bivariate polynomial splines, and we discuss the general setting where local mesh adaptivity is combined with local polynomial degree adaptivity ...
A non-uniform degree C 1 spline space consisting of quadratic and cubic polynomial pieces is built on the above mesh. ...
arXiv:1903.05949v1
fatcat:xb24jzijlzhulgadhn2nh7firy
Polynomial spline spaces of non-uniform bi-degree on T-meshes: combinatorial bounds on the dimension
2021
Advances in Computational Mathematics
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The latter allows for the flexibility of choosing non-uniform bi-degrees for the splines, i.e., different bi-degrees on different faces of the T-mesh. ...
Focusing on T-meshes, we study the dimension of the space of bivariate polynomial splines, and we discuss the general setting where local mesh adaptivity is combined with local polynomial degree adaptivity ...
To define a non-uniform degree spline space on T , we need as input a degreedeficit distribution that will later help us specify non-uniform degrees on T . ...
doi:10.1007/s10444-020-09829-4
fatcat:marw6xov7jaxhaspnhtzwfsyqm
Non-uniform embedding applications for synchronization analysis
2016
Journal of Vibroengineering
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For time delay kernel estimation, a non-uniform embedding was used. Evolutionary optimization algorithms were introduced for non-uniform time delay identification. ...
Iterative polynomial model for synchronization of vibrations was proposed. A polynomial was constructed using time delay coordinates. ...
This technique is based on combination of non-uniform embedding, evolutionary optimization algorithms and polynomial model. ...
doi:10.21595/jve.2016.18090
fatcat:lbrs7jp5dvbonkmyqgujksr6de
Uniform characterizations of non-uniform complexity measures
1985
Information and Control
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Non-uniform complexity measures originated in automata and formal languages theory are characterized in terms of well-known uniform complexity classes. ...
It is shown to be closely related to context-free cost, boolean circuits, straight line programs, and Turing machines with sparse oracles and time or space bounds. ...
It is not known whether restricting boolean circuits to gates of fan-out one restricts the polynomial non-uniform class. ...
doi:10.1016/s0019-9958(85)80026-7
fatcat:4kpvj2xa6fb25okxhykiyytpbe
Polynomial generation and quasi-interpolation in stationary non-uniform subdivision
2003
Computer Aided Geometric Design
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We show that these conditions hold in the context of non-uniform subdivision as well, and we demonstrate how they can be used for the construction of stationary non-uniform subdivision schemes that have ...
We study the necessary and sufficient conditions for the generation of polynomials by stationary subdivision schemes, and we show how to derive appropriate quasiinterpolation rules that have the optimal ...
scheme can be defined on a non-uniform grid X. ...
doi:10.1016/s0167-8396(03)00006-2
fatcat:vvm7iv5jwrbi7ohfmnhpvldnhq
Pyramid Algorithms for Bernstein--Bézier Finite Elements of High, Nonuniform Order in Any Dimension
2014
SIAM Journal on Scientific Computing
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A new, non-uniform order, variant of the de Casteljau algorithm is developed that is applicable to the variable polynomial order case but incurs no additional complexity compared with the original algorithm ...
Pyramid algorithms replace an operation on single high order polynomial by a recursive sequence of self-similar affine combinations, and are ubiquitous in CAGD for computations involving high order curves ...
How about the choice of a basis for the non-uniform order space? ...
doi:10.1137/130914048
fatcat:pyrgyigq6zdyhnq55j7axldjxy
Introducing a Space Complexity Measure for P Systems
2009
International Journal of Computers Communications & Control
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We define space complexity classes in the framework of membrane computing, giving some initial results about their mutual relations and their connection with time complexity classes, and identifying some ...
Since |f (x)| ≤ poly(n), M operates in polynomial time and Π f (x) in polynomial space; but then Π = {Π f (x) | x ∈ Σ } is a polynomially semi-uniform family of P systems deciding L in polynomial space ...
The definitions are analogous in the uniform and non-confluent cases. ...
doi:10.15837/ijccc.2009.3.2779
fatcat:xutk47k535fxzk4gzqkdo4slpy
Small-Space Analogues of Valiant's Classes
[chapter]
2009
Lecture Notes in Computer Science
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We introduce the class VL as an algebraic variant of deterministic log-space L. In the uniform setting, we show that our definition coincides with that of VPSPACE at polynomial width. ...
Further, to define algebraic variants of non-deterministic space-bounded classes, we introduce the notion of "read-once" certificates for arithmetic circuits. ...
This is because the corresponding log-space class in this model will be computing only sparse polynomials, but in the non-uniform setting sparse polynomials are known to be contained in a highly restrictive ...
doi:10.1007/978-3-642-03409-1_23
fatcat:4kfukithbrf7nlpmuhec7hd5v4
A SYNTHESIS OF UNEQUALLY SPACED ANTENNA ARRAYS USING LEGENDRE FUNCTIONS
2009
Progress In Electromagnetics Research M
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The determination of the optimal excitation and spacing is shown to be a polynomial problem; this is described in terms of a unified mathematical approach to nonlinear optimization of multidimensional ...
For the optimization of the array pattern, it is proposed to adjust both the excitation and the spacing of the antenna elements. ...
non-uniform spacing in a planar array are given in the next Section. ...
doi:10.2528/pierm09032305
fatcat:4kk3zwj56vh2nftpdwza3ase3m
Compensating for non-uniform screens in projection display systems
2009
Color Imaging XIV: Displaying, Processing, Hardcopy, and Applications
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on the order of polynomial used for regression. ...
In this research, two different methods of linearization as well as the use of polynomial regression up to fourth order have been investigated, based both on the standard deviation and the average of color ...
Based on the experimental data we see that 50-70 percent improved non-uniformity in terms of average color differences is achieved using regression in CIELAB space. ...
doi:10.1117/12.810493
dblp:conf/clrimg/RenaniTH09
fatcat:4mhorjf7hje4dhxovpka55e45u
Anisotropic spline approximation with non-uniform B-splines
2016
Applicable Analysis
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2016 pre-print arXiv:1601.05275v3 fatcat:s66leezgivgnbfcln6cq35t3caOther Versions
Reif introduced the concept of diversification of uniform tensor product B-splines. Based on this concept, we give a new constructive modification of non-uniform B-splines. ...
The resulting spline spaces are perfectly fitted for the approximation of functions defined on domains Ω⊂R^2. ...
The representation of polynomials in terms of non-uniform splines is slightly different from the representation in the uniform case. ...
doi:10.1080/00036811.2016.1254774
fatcat:7pf3gycrh5bjtnezsgvqitsnri
Page 2120 of Mathematical Reviews Vol. , Issue 2004c
[page]
2004
Mathematical Reviews
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[Levin, Adi] Polynomial generation and quasi-interpolation in stationary non-uniform subdivision. (English summary) Comput. Aided Geom. Design 20 (2003), no. 1, 41-60. ...
Summary: “Interpolation on non-uniformly distributed roots of unity has received quite some attention lately. ...
Tent pitching and Trefftz-DG method for the acoustic wave equation
[article]
2019
arXiv
pre-print
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2021 accepted arXiv:1907.02367v3 fatcat:go4zrn75hnaepoxrqxzvsq2t2aOther Versions
We present a space-time Trefftz discontinuous Galerkin method for approximating the acoustic wave equation semi-explicitly on tent pitched meshes. ...
The method is implemented in NGSolve, solving the space-time elements in parallel, whenever possible. ...
Figure 9 : 9 The convergence rates on uniform and non-uniform meshes and timings (bottom) with the singular initial condition (top). ...
arXiv:1907.02367v2
fatcat:phftt6dqxnfcndkdbx7hzzt2ey
Alternative space definitions for P systems with active membranes
2021
Journal of Membrane Computing
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AbstractThe first definition of space complexity for P systems was based on a hypothetical real implementation by means of biochemical materials, and thus it assumes that every single object or membrane ...
requires some constant physical space. ...
Since |f (x)| is bounded by a polynomial, M ′ operates in polynomial time and f (x) in polynomial binary space; it follows that � = { f (x) | x ∈ ⋆ } is a polynomially semi-uniform family of P systems ...
doi:10.1007/s41965-021-00074-2
fatcat:oqi2esvyibdbdmz37zun7ve7mu
Asymptotic Smoothness, Convex Envelopes and Polynomial Norms
[article]
2016
arXiv
pre-print
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We introduce a suitable notion of asymptotic smoothness on infinite dimensional Banach spaces, and we prove that, under some structural restrictions on the space, the convex envelope of an asymptotically ...
Furthermore, we study convexity and smoothness properties of polynomial norms, and we obtain that a polynomial norm of degree N has modulus of convexity of power type N. ...
Note in particular that the usual supnorm f (x) = x ∞ on the space c 0 is an example of non-differentiable function which is asymptotically p-smooth for every p > 1. ...
arXiv:1512.05407v2
fatcat:kb5ojuuvczdw3pol3cxg4jasiq
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