Bounds on the dimensions of trivariate spline spaces

نویسندگان

  • Peter Alfeld
  • Larry L. Schumaker
چکیده

We derive upper and lower bounds on the dimensions of trivariate spline spaces defined on tetrahedral partitions. The results hold for general partitions, and for all degrees of smoothness r and polynomial degrees d.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the dimension of spline spaces on triangulations

We consider, from an algebro-geometric perspective, the problem of determining the dimension of the space of bivariate and trivariate piecewise polynomial functions (or splines) defined on triangular and tetrahedral partitions. Classical splines on planar rectangular grids play an important role in Computer Aided Geometric Design, and splines spaces over arbitrary subdivisions of planar domains...

متن کامل

Bounds on the Dimension of Trivariate Spline Spaces: A Homological Approach

We consider the vector space of globally differentiable piecewise polynomial functions defined on a three-dimensional polyhedral domain partitioned into tetrahedra. We prove new lower and upper bounds on the dimension of this space by applying homological techniques. We give an insight of different ways of approaching this problem by exploring its connections with the Hilbert series of ideals g...

متن کامل

Dynamic Relationship Between Macroeconomic Instability and Private Investment in the Iranian Economy

This paper investigates the relationship between macroeconomic instability and private investment of the Iranian economy. The study uses a trivariate VAR(2)-GARCH(1,1)-in-Mean with diagonal BEKK approach to proxied inflation and exchange rate uncertainties as the main indicators of macroeconomic instability. Moreover, Bounds testing approach to level relationship applied to investigate the long...

متن کامل

Construction of Trivariate Compactly SupportedBiorthogonal Box Spline

abstract We give a formula for the duals of the mask associated with trivariate box spline functions. We show how to construct trivariate nonseparable compactly supported biorthogonal wavelets associated with box spline functions. The biorthogonal wavelets may have arbitrarily high regularities.

متن کامل

Three topics in multivariate spline theory

We examine three topics at the interface between spline theory and algebraic geometry. In the first part, we show how the concept of domain points can be used to give an original explanation of Dehn–Sommerville equations relating the numbers of i-faces of a simplicial polytope in R, i = 0. . . . , n − 1. In the second part, we echo some joint works with T. Sorokina and with P. Clarke on computa...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Adv. Comput. Math.

دوره 29  شماره 

صفحات  -

تاریخ انتشار 2008