Bivariate cubic spline space and bivariate cubic NURBS surfaces

2004 ◽  
Author(s):  
Chong-Jun Li ◽  
Ren-Hong Wang
Keyword(s):  
Cubic Spline ◽  
Spline Space ◽  
Nurbs Surfaces ◽  
Bivariate Cubic Spline

On splitting for cubic spline wavelets with four zero moments on an interval

2021 ◽  
pp. 72-87
Author(s):  
Борис Михайлович Шумилов
Keyword(s):  
Cubic Spline ◽  
Spline Space ◽  
Dirichlet Boundary Conditions ◽  
Second Derivative ◽  
Algebraic Equations ◽  
Splitting Algorithm ◽  
Spline Wavelets ◽  
Wavelet Space ◽  
Linear Algebraic Equations ◽  
The Stability

В пространстве кубических сплайнов построены вейвлеты, удовлетворяющие однородным граничным условиям Дирихле и обнулению первых четырех моментов. Получены неявные соотношения, связывающие сплайн-коэффициенты разложения на начальном уровне со сплайн-коэффициентами и вейвлет-коэффициентами на вложенном уровне ленточной системой линейных алгебраических уравнений с невырожденной матрицей. После расщепления на четные и нечетные уравнения матрица преобразования имеет пять (вместо трех в случае двух нулевых моментов) диагоналей. Доказано наличие строгого диагонального доминирования по столбцам. Для сравнения использованы вейвлеты с двумя нулевыми моментами и интерполяционные кубические сплайновые вейвлеты. Результаты численных экспериментов показывают, что схема с четырьмя нулевыми моментами точнее при аппроксимации функций, но грубее при аппроксимации второй производной. The article examines the problem of constructing a splitting algorithm for cubic spline wavelets. First, a cubic spline space is constructed for splines with homogeneous Dirichlet boundary conditions. Then, using the first four zero moments, the corresponding wavelet space is constructed. The resulting space consists of cubic spline wavelets that satisfy the orthogonality conditions for all thirddegree polynomials. The originality of the research lies in obtaining implicit relations connecting the coefficients of the spline expansion at the initial level with the spline coefficients and wavelet coefficients at the embedded level by a band system of linear algebraic equations with a nondegenerate matrix. Excluding the even rows of the system, the resulting transformation algorithm is obtained as a solution to a sequence of band systems of linear algebraic equations with five (instead of three in the case of two zero moments) diagonals. The presence of strict diagonal dominance over the columns is proved, which confirms the stability of the computational process. For comparison, we adopt the results of calculations using wavelets orthogonal to first-degree polynomials and interpolating cubic spline wavelets with the property of the best mean-square approximation of the second derivative of the function being approximated. The results of numerical experiments show that the scheme with four zero moments is more accurate in the approximation of functions, but becomes inferior in accuracy to the approximation of the second derivative.

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.

Glucose Calibration Modeling in Blood with Spline Regression Approaching to Non-Invasive Tools

2018 ◽  
pp. 144-149
Author(s):  
Ria Hayatun Nur ◽  
Indahwati A ◽  
Erfiani A
Keyword(s):  
Diabetes Mellitus ◽  
Linear Regression ◽  
Good Health ◽  
Cubic Spline ◽  
The Body ◽  
Spline Regression ◽  
Linear Quadratic ◽  
Important Thing ◽  
Non Invasive

In this globalization era, health is the most important thing to be able to run various activities. Without good health, this will hinder many activities. Diabetes mellitus is one of the diseases caused by unhealty lifestyle.There are many treatments that can be done to prevent the occurrence of diabetes. The treatments are giving the insulin and also checking the glucose rate to the patients.Checking the glucose rate needs the tools which is safety to the body. This research want to develop non invasive tool which is safety and do not injure the patient. The purpose of this research is also finding the best model which derived from Linear, Quadratic, and Cubic Spline Regression. Some respondents were taking to get the glucose measuring by invasive and non invasive tools. It could be seen clearly that Spline Linear Regression was the best model than Quadratic and Cubic Spline Regression. It had 70% and 33.939 for R2 and RMSEP respectively.

ACCURACY OF RIVER GEOMETRY INTERPOLATION USING CUBIC SPLINE CURVE AT ALB MISSING AREA AND INFULUENCE OF FLOW REGIME

2018 ◽  
Vol 74 (4) ◽  
pp. I_859-I_864
Author(s):  
Takayuki OKABE ◽  
Takanori YAMAZAKI ◽  
Atsumasa OZAWA ◽  
Shinichi MORITA ◽  
Shigeo HORIUCHI ◽  
...  
Keyword(s):  
Flow Regime ◽  
Cubic Spline ◽  
Spline Curve ◽  
Cubic Spline Curve
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