We use a set of basis functions such as sinusoids or B-spline functions to replace the space-variant (local) parameters with space-invariant (global) ... R Abdolee,B Champagne,Ali H. Sayed - Statistical Signal Processing Workshop 被引量: 25发表: 2012年 General discrete centered image pyram...
Orthogonal cubic spline basis functionB-splineGram–Schmidt processPartial integro-differential equationWeakly singular kernelIn this paper, a new orthogonal basis for the space of cubic splines has been introduced. This basis is obtained based on B-splines and using the Gram鈥揝chmidt ...
(12.139b) is now given by (12.143e)Cρ(x,xI)=∑α=1lqα(x,x)qα(xI,x)⟨qα,qα⟩x˜, which can be used in Eqs. (12.139c) and (12.139d) to give the global approximation formulations based on the orthogonal basis in Eq. (12.143a). The Lagrangian polynomial (Waring, ...
A fourth-order orthogonal spline collocation method to fourth-order boundary value problemsOrthogonal cubic spline collocation methods (OCSCM)fourth-order linear and nonlinear boundary value problemSwift–Hohenberg equationcubic monomial basis functions
Daub CO, Steuer R, Selbig J, Kloska S: Estimating mutual information using B-spline functions- an improved similarity measure for analyzing gene expression data. BMC Bioinformatics 2004, 5: 118. 10.1186/1471-2105-5-118 Article PubMed Central PubMed Google Scholar Perou CM, Sorlie T, Eisen...
Analysis of spline methods for the smooth solution u on uniform mesh In this section, we assume that u(x,t)∈Cx,t6,2(Ω) is a unique smooth solution of problem (1)–(3), where Ω=[a,b]×[0,T]. When α=1, problem (1)–(3) reduces to the classical parabolic equation [55]...
Surface fitting for interactive shape design A method is presented to create smooth B- spline surfaces on basis of three-dimensional data points. The intended application is interactive shape design a... JSM Vergeest - 《Computers in Industry》 被引量: 20发表: 1989年 ...
In this work, we consider the following one-dimensional fractional sub-diffusion equation c 0 D α t u(x, t) =d ∂ 2 u(x, t) ∂x 2 + f (x, t), x ∈ (a, b), t ∈ (0, T ], (1) u(x, 0) =ψ(x), x ∈ (a, b), (2) u(a, t) = w(t), u(b, t)...
Values of the fracture pressure between the collocation points can then be calculated by employing an interpolation scheme, such as the Lagrange interpolation (B Vaferi et al., 2012). Eq. (24) illustrates the values of pfD which are obtained using the Lagrange interpolation scheme.(24)pfD=∑...
Fig. 19. Average computational time required to predict a shape for a given number of principal components: (a) cubic spline interpolation, (b) 2nd-order diffuse approximation. The dashed lines correspond to the average value ± the standard deviation. The computational time is 1000 times smaller...