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Polynomial spline spaces of non-uniform bi-degree on T-meshes: Combinatorial bounds on the dimension [article]

Deepesh Toshniwal, Thomas Hughes
2019 arXiv   pre-print
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

Deepesh Toshniwal, Bernard Mourrain, Thomas J. R. Hughes
2021 Advances in Computational Mathematics  
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

Migle Drulyte, Kristina Lukoseviciute, Jurate Ragulskiene
2016 Journal of Vibroengineering  
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

José L. Balcázar, Josep Díaz, Joaquim Gabarró
1985 Information and Control  
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

A. Levin
2003 Computer Aided Geometric Design  
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

Mark Ainsworth
2014 SIAM Journal on Scientific Computing  
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

Antonio E. Porreca, Alberto Leporati, Giancarlo Mauri, Claudio Zandron
2009 International Journal of Computers Communications & Control  
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]

Meena Mahajan, B. V. Raghavendra Rao
2009 Lecture Notes in Computer Science  
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


Jorge Sanchez, David H. Covarrubias-Rosales, Marco A. Panduro
2009 Progress In Electromagnetics Research M  
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

Siavash Asgari Renani, Masato Tsukada, Jon Yngve Hardeberg, Reiner Eschbach, Gabriel G. Marcu, Shoji Tominaga, Alessandro Rizzi
2009 Color Imaging XIV: Displaying, Processing, Hardcopy, and Applications  
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

N. Sissouno
2016 Applicable Analysis  
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  
[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]

Ilaria Perugia, Joachim Schöberl, Paul Stocker, Christoph Wintersteiger
2019 arXiv   pre-print
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

Artiom Alhazov, Alberto Leporati, Luca Manzoni, Giancarlo Mauri, Claudio Zandron
2021 Journal of Membrane Computing  
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]

Jesús A. Jaramillo, Raquel Gonzalo, Diego Yáñez
2016 arXiv   pre-print
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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