Cardinal Splines

1988 ◽  
pp. 164-166 ◽  
Author(s):  
Carl de Boor
Keyword(s):  
Cardinal Splines

Identification of Viscously Damped Distributed Structural Dynamic Systems

1991 ◽  
Author(s):  
R. Chander ◽  
M. Meyyappa ◽  
S. Hanagud
Keyword(s):  
Dynamic Systems ◽  
Beam Theory ◽  
Continuous Functions ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Structural Dynamic ◽  
Domain Identification ◽  
Forcing Function ◽  
Cardinal Splines ◽  
Stiffness And Damping

Abstract A frequency domain identification technique applicable to damped distributed structural dynamic systems is presented. The technique is developed for beams whose behavior can be modeled using the Euler-Bernoulli beam theory. External damping of the system is included by means of a linear viscous damping model. Parameters to be identified, mass, stiffness and damping distributions are assumed to be continuous functions over the beam. The response at a discrete number of points along the length of the beam for a given forcing function is used as the data for identification. The identification scheme involves approximating the infinite dimensional response and parameter spaces by using quintic B-splines and cubic cardinal splines, respectively. A Galerkin type weighted residual procedure, in conjunction with the least squares technique, is employed to determine the unknown parameters. Numerically simulated response data for an applied impulse load are utilized to validate the developed technique. Estimated values for the mass, stiffness and damping distributions are discussed.

scholarly journals Solving Systems of Volterra Integral Equations with Cardinal Splines

2015 ◽  
Vol 03 (11) ◽  
pp. 1422-1430 ◽  
Author(s):  
Xiaoyan Liu ◽  
Zhi Liu ◽  
Jin Xie
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Cardinal Splines

On the convergence of cardinal splines

2020 ◽  
Vol 48 (1) ◽  
pp. 508-512 ◽  
Author(s):  
W.R. Madych
Keyword(s):  
Cardinal Splines

Recovery of band limited functions via cardinal splines

2001 ◽  
Vol 44 (9) ◽  
pp. 1126-1131 ◽  
Author(s):  
Gensun Fang
Keyword(s):  
Cardinal Splines ◽  
Band Limited

scholarly journals Modeling and refactoring the indigo patterns

2019 ◽  
Vol 14 ◽  
pp. 155892501988397
Author(s):  
Chen Tao ◽  
Jialiang Lu ◽  
Miao Su ◽  
Xinghua Hong
Keyword(s):  
Contour Tracing ◽  
Geometric Center ◽  
Complex Element ◽  
Hu Moments ◽  
Model Instance ◽  
Cardinal Splines ◽  
In Virtue Of

For purpose of reconstruction and innovation of indigo patterns, this study explores modeling, reconstruction, and assembling of the pattern elements by means of mathematics. A model for indigo pattern elements is proposed based on cardinal splines, in which the rigidity of shape is conveyed by the tension coefficient, and the concavity and variety by configuration of the knots. The generalized version of this model is capable of covering any complex element. The contour tracing technique is employed to extract pattern elements from the image, and the closest model instance is selected in virtue of invariance of the improved Hu moments. The selected instances are transformed with respect to the geometric center, the coverage, and the coincidence to match the pattern elements in the image so as to reconstruct the whole pattern. The element filters are conducted on the reconstructed patterns to modify the elements and produce new innovative patterns of constant skeleton. The model is borrowed serving as a skeleton in element assembling. The skeleton properties are investigated to provide basis for skeleton embodiment in which these properties are involved into establishing the placement determiner and element determiner so as to carry out the assembling of elements. Also discussed is the extended skeleton which goes beyond the model and brings about variety and flexibility to element assembling. It is turned out that reconstruction with the model well implements a mathematical copy of the pattern, and the assembling of elements by skeletons provides rich possibilities to innovation of indigo patterns.

scholarly journals The Cardinal Spline Methods for the Numerical Solution of Nonlinear Integral Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xiaoyan Liu ◽  
Jin Xie ◽  
Zhi Liu ◽  
Jiahuan Huang
Keyword(s):  
Integral Equations ◽  
High Accuracy ◽  
Spline Functions ◽  
Sufficient Condition ◽  
Nonlinear Integral Equations ◽  
Effective Technique ◽  
Original Solution ◽  
Cardinal Spline ◽  
The Matrix ◽  
Cardinal Splines

In this study, an effective technique is presented for solving nonlinear Volterra integral equations. The method is based on application of cardinal spline functions on small compact supports. The integral equation is reduced to a system of algebra equations. Since the matrix for the system is triangular, it is relatively straightforward to solve for the unknowns and an approximation of the original solution with high accuracy is accomplished. Several cardinal splines are employed in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined, and the convergence rate is analyzed. We compare our method with other methods proposed in recent papers and demonstrated the advantage of our method with several examples.

On Cardinal Spline Interpolation

2013 ◽  
Vol 13 (1) ◽  
pp. 39-54
Author(s):  
Rolf D. Grigorieff
Keyword(s):  
Unique Solution ◽  
Error Estimates ◽  
Interpolation Problem ◽  
Polynomial Growth ◽  
Spline Interpolation ◽  
Cardinal Spline ◽  
Cardinal Splines ◽  
Cardinal Spline Interpolation

Abstract. In the present paper it is shown that the interpolation problem for multiple knot cardinal splines subject to general interpolation conditions has a unique solution with polynomial growth if the data grow correspondingly provided a certain determinantal condition is satisfied. An application to Hs error estimates for the interpolation with periodic multiple knot splines is given.

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