On the refinement matrix mask of interpolating Hermite splines

2020 ◽  
Vol 109 ◽  
pp. 106524
Author(s):  
Lucia Romani ◽  
Alberto Viscardi
Keyword(s):  
Hermite Splines

scholarly journals A New Approach of Constrained Interpolation Based on Cubic Hermite Splines

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
J. Saeidian ◽  
M. Sarfraz ◽  
A. Azizi ◽  
S. Jalilian
Keyword(s):  
Linear Programming ◽  
Constrained Interpolation ◽  
New Approach ◽  
Theoretical Support ◽  
Suitable Function ◽  
Hermite Splines

Suppose we have a constrained set of data and wish to approximate it using a suitable function. It is natural to require the approximant to preserve the constraints. In this work, we state the problem in an interpolating setting and propose a parameter-based method and use the well-known cubic Hermite splines to interpolate the data with a constrained spline to provide with a C 1 interpolant. Then, more smoothing constraints are added to obtain C 2 continuity. Additionally, a minimization criterion is presented as a theoretical support to the proposed study; this is performed using linear programming. The proposed methods are demonstrated with illustrious examples.

scholarly journals Support and approximation properties of Hermite splines

2020 ◽  
Vol 368 ◽  
pp. 112503 ◽  
Author(s):  
Julien Fageot ◽  
Shayan Aziznejad ◽  
Michael Unser ◽  
Virginie Uhlmann
Keyword(s):  
Approximation Properties ◽  
Hermite Splines

scholarly journals Multiwavelet Frames in Signal Space Originated From Hermite Splines

2007 ◽  
Vol 55 (3) ◽  
pp. 797-808 ◽  
Author(s):  
Amir Z. Averbuch ◽  
Valery A. Zheludev ◽  
Tamir Cohen
Keyword(s):  
Signal Space ◽  
Hermite Splines

scholarly journals The Application of the Collocation Method Using Hermite Cubic Splines to Nonlinear Transient One-Dimensional Heat Conduction Problems

1975 ◽  
Vol 97 (4) ◽  
pp. 562-569 ◽  
Author(s):  
T. C. Chawla ◽  
G. Leaf ◽  
W. L. Chen ◽  
M. A. Grolmes
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Finite Difference ◽  
Differential Equations ◽  
Collocation Method ◽  
Gaussian Quadrature ◽  
Time Step ◽  
One Dimensional ◽  
Hermite Splines ◽  
Nonlinear Transient

A collocation method for the solution of one-dimensional parabolic partial differential equations using Hermite splines as approximating functions and Gaussian quadrature points as collocation points is described. The method consists of expanding dependent variables in terms of piece-wise cubic Hermite splines in the space variable at each time step. The unknown coefficients in the expansion are obtained at every time step by requiring that the resultant differential equation be satisfied at a number of points (in particular at the Gaussian quadrature points) in the field equal to the number of unknown coefficients. This collocation procedure reduces the partial differential equation to a system of ordinary differential equations which is solved as an initial value problem using the steady-state solution as the initial condition. The method thus developed is applied to a two-region nonlinear transient heat conduction problem and compared with a finite-difference method. It is demonstrated that because of high-order accuracy only a small number of equations are needed to produce desirable accuracy. The method has the desirable characteristic of an analytical method in that it produces point values as against nodal values in the finite-difference scheme.

On cubic formulas related to the mixed Hermite splines

1993 ◽  
Vol 45 (4) ◽  
pp. 629-632 ◽  
Author(s):  
Zh. E. Myrzanov
Keyword(s):  
Hermite Splines
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