scholarly journals Cell reducing and the dimension of the C^1 bivariate spline space

2021 ◽  
Author(s):  
Gašper Jaklič
Keyword(s):  
Spline Space ◽  
Bivariate Spline

scholarly journals A Note on the Dimension of the Bivariate Spline Space over the Morgan--Scott Triangulation

2000 ◽  
Vol 37 (3) ◽  
pp. 1021-1028 ◽  
Author(s):  
Jian Song Deng ◽  
Yu Yu Feng ◽  
Jernej Kozak
Keyword(s):  
Spline Space ◽  
Bivariate Spline

On the Dimension of Bivariate C1 Cubic Spline Space with Homogeneous Boundary Conditions over a CT Triangulation

2011 ◽  
Vol 50-51 ◽  
pp. 488-492
Author(s):  
Dian Xuan Gong ◽  
Feng Gong Lang
Keyword(s):  
Boundary Conditions ◽  
Computer Aided Design ◽  
Numerical Approximation ◽  
Cubic Spline ◽  
Spline Space ◽  
Singular Boundary ◽  
Piecewise Polynomial ◽  
Nite Element ◽  
Bivariate Spline ◽  
Aided Design

A bivariate spline is a piecewise polynomial with some smoothness de ned on a parti- tion. In this paper, we mainly study the dimensions of bivariate C1 cubic spline spaces S1;0 3 (CT ) and S1;1 3 (CT ) with homogeneous boundary conditions over CT by using interpolating technique, where CT stands for a CT triangulation. The dimensions are related with the numbers of the inter vertices and the singular boundary vertices. The results of this paper can be applied in many elds such as the nite element method for partial di erential equation, computer aided design, numerical approximation, and so on.

scholarly journals Use of Spline Functions for Premium Rating by Geographic Area

1989 ◽  
Vol 19 (1) ◽  
pp. 91-122 ◽  
Author(s):  
G. C. Taylor
Keyword(s):  
Goodness Of Fit ◽  
Geographic Area ◽  
Spline Functions ◽  
Bivariate Splines ◽  
Contour Maps ◽  
Bivariate Spline ◽  
Spline Surfaces ◽  
Insurance Portfolio ◽  
Selection Of

AbstractThe paper gives details of a case study in the premium rating of a Householders Contents insurance portfolio. The rating is performed by the fitting of bivariate spline functions to a version of operating ratio described in Section 3.The use of bivariate splines requires a small amount of mathematical equipment, which is developed in Section 4. The fitting of splines, using regression is carried out in Sections 5 and 6, where the numerical results are given, including some assessment of goodness-of-fit.Contour maps of the spline surfaces are also given, and used for the selection of geographic areas used for premium rating purposes. These are compared with the areas, past and present, actually used by the insurer concerned.

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