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Search Results: 1 - 10 of 103 matches for " splines "
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Approximation by Splines of Hermite Type  [PDF]
Yuri K. Dem’yanovich, Irina G. Burova
Applied Mathematics (AM) , 2013, DOI: 10.4236/am.2013.411A3002

The approximation evaluations by polynomial splines are well-known. They are obtained by the similarity principle; in the case of non-polynomial splines the implementation of this principle is difficult. Another method for obtaining of the evaluations was discussed earlier (see [1]) in the case of nonpolynomial splines of Lagrange type. The aim of this paper is to obtain the evaluations of approximation by non-polynomial splines of Hermite type. Considering a linearly independent system of column-vectors\"\", \"\". Let \"\" be square matrix. Supposing that \"\" and \"\" are columns with components from the linear space \"\" such that \"\". Let \"\" be vector with components \"\" belonging to conjugate space \"\". For an element \"\" we consider a linear combination of elements \"\" By definition, put \"\". The discussions are based on the next assertion. The following relation holds: \"\" where the second factor on the right-hand side is the determinant of a block-matrix of order m + 2. Using this assertion, we get the representation of residual of approximation by minimal splines of Hermite type. Taking into account the representation,

On the Implementation of Exponential B-Splines by Poisson Summation Formula  [PDF]
Sinuk Kang
Journal of Applied Mathematics and Physics (JAMP) , 2016, DOI: 10.4236/jamp.2016.44072

Polynomial splines have played an important role in image processing, medical imaging and wavelet theory. Exponential splines which are of more general concept have been recently investigated.We focus on cardinal exponential splines and develop a method to implement the exponential B-splines which form a Riesz basis of the space of cardinal exponential splines with finite energy.

Local Influence Analysis of Varying-Coefficient Model with Random Right Censorship  [PDF]
Shuling Wang, Man Liu, Daqing Liao, Ting Wang
Applied Mathematics (AM) , 2013, DOI: 10.4236/am.2013.45117

For this model, this paper studies the method and application of the diagnostic mostly. Firstly, the primary model is transformed to varying-coefficient model by using a general transformation method. Secondly, a simple estimation form of the coefficient functions is obtained by employing the B spline. Then, local influence is discussed and concise influence matrix is obtained. At last, an example is given to illustrate our results.

Modeling of Objects Using Conic Splines  [PDF]
Muhammad Sarfraz, Malik Z. Hussain, Munazah Ishaq
Journal of Software Engineering and Applications (JSEA) , 2013, DOI: 10.4236/jsea.2013.63B015
Abstract: This paper contributes towards modeling for the designing of objects in the areas of Computer Graphics (CG), Computer-Aided Design (CAD), Computer-Aided Manufacturing (CAM), and Computer-Aided Engineering (CAE). It provides a modeling technique for the designing of objects. The model is based on a conic-like curve (rational quadratics) method and provides an extra degree of freedom to the user to fine tune the shape of the design to the satisfactory level. The 2D curve model has then been extended for the designing of 3D objects to produce fancy objects. The scheme has been also extended to automate the degree of freedom when a reverse engineering is required for images of the objects. A heuristic technique of genetic algorithm is applied to find optimal values of shape parameters in the description of conics.
A Study on B-Spline Wavelets and Wavelet Packets  [PDF]
Sana Khan, Mohammad Kalimuddin Ahmad
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.519287
Abstract: In this paper, we discuss the B-spline wavelets introduced by Chui and Wang in [1]. The definition for B-spline wavelet packets is proposed along with the corresponding dual wavelet packets. The properties of B-spline wavelet packets are also investigated.
La obtención y proyección de tablas de mortalidad empleando curvas spline
Mina-Valdés, Alejandro;
Papeles de población , 2011,
Abstract: one of the tools of numerical analysis is the use of polynomials of nth order to interpolate between n+1 points, taking cases where these polynomial functions can lead to erroneous results. an alternative is to implement polynomials of lesser order than the subsets of data. these connected polynomials are called functions of segmental interpolation (spline functions). this article introduces the tool provided by numerical analysis as a technical instrument needed to carry out all existing mathematical procedures based on algorithms to enable its simulation or calculation, in particular, the functions spline defined in ranges (by sections), with interpolation through them, giving rise to the adjustment of spline curves based on surviving an abbreviated table of mexican mortality lx series in order to disaggregate by age deployed, respecting the cavities that because of the effect of mortality in the early and following ages appear in the mexican experience. also using splines the simulations that allow obtaining future scenarios of the surviving lx series produces the mexican mortality for the years 2010-2050, projections that generate complete tables of mortality for men and women of this period, highlighting the differences between sexes and ages of their chances to survive and increments in life expectancy.
Automatic smoothing by optimal splines
Biloti, Ricardo;Santos, Lúcio T.;Tygel, Martin;
Revista Brasileira de Geofísica , 2003, DOI: 10.1590/S0102-261X2003000200006
Abstract: we propose a method that is capable to filter out noise as well as suppress outliers of sampled real functions under fairly general conditions. from an a priori selection of the number of knots that define the adjusting spline, but not their location in that curve, the method automatically determines the adjusting cubic spline in a least-squares optimal sense. the method is fast and easily allows for selection of various possible number of knots, adding a desirable flexibility to the procedure. as an illustration, we apply the method to some typical situations found in geophysical problems.
Shifted Linear Interpolation Filter  [PDF]
Hannu Olkkonen, Juuso T. Olkkonen
Journal of Signal and Information Processing (JSIP) , 2010, DOI: 10.4236/jsip.2010.11005
Abstract: Linear interpolation has been adapted in many signal and image processing applications due to its simple implementation and low computational cost. In standard linear interpolation the kernel is the second order B-spline. In this work we show that the interpolation error can be remarkably diminished by using the time-shifted B-spline as an interpolation kernel. We verify by experimental tests that the optimal shift is. In VLSI and microprocessor circuits the shifted linear interpolation (SLI) algorithm can be effectively implemented by the z-transform filter. The interpolation error of the SLI filter is comparable to the more elaborate higher order cubic convolution interpolation.
Contour Based Path Planning with B-Spline Trajectory Generation for Unmanned Aerial Vehicles (UAVs) over Hostile Terrain  [PDF]
Ee-May Kan, Meng-Hiot Lim, Swee-Ping Yeo, Jiun-Sien Ho, Zhenhai Shao
Journal of Intelligent Learning Systems and Applications (JILSA) , 2011, DOI: 10.4236/jilsa.2011.33014
Abstract: This research focuses on trajectory generation algorithms that take into account the stealthiness of autonomous UAVs; generating stealthy paths through a region laden with enemy radars. The algorithm is employed to estimate the risk cost of the navigational space and generate an optimized path based on the user-specified threshold altitude value. Thus the generated path is represented with a set of low-radar risk waypoints being the coordinates of its control points. The radar-aware path planner is then approximated using cubic B-splines by considering the least radar risk to the destination. Simulated results are presented, illustrating the potential benefits of such algorithms.
Cubic Spline Approximation for Weakly Singular Integral Models  [PDF]
Franca Caliò, Elena Marchetti
Applied Mathematics (AM) , 2013, DOI: 10.4236/am.2013.411211
Abstract: In this paper we propose a numerical collocation method to approximate the solution of linear integral mixed Volterra Fredholm equations of the second kind, with particular weakly singular kernels. The collocation method is based on the class of quasi-interpolatory splines on locally uniform mesh. These approximating functions are particularly suitable to tackle on problems with weakly regular solutions. We analyse the convergence problems and we present some numerical results and comparisons to confirm the efficiency of the numerical model.
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