In this paper, an innovative neural-network architecture is proposed and elucidated. This architecture, based on the Kolmogorov's superposition theorem (1957) and called the Kolmogorov's spline network (KSN), utilizes more degrees of adaptation to data than currently used neural-network architectures (NNAs). By using cubic spline technique of approximation, both for activation and internal func...

We propose a new method called C-SOM for function approximation. C-SOM extends the standard Self-Organizing Map (SOM) with a combination of Local Linear Mapping (LLM) and cubic spline based interpolation techniques to improve standard SOMs' generalization capabilities. CSOM uses the gradient information provided by the LLM technique to compute a cubic spline interpolation in the input space bet...

In this paper, We use the wavelet bases of Hermite cubic splines to solve the second kind integral equations xCi) -11 K(t,s)x(s)ds = y(t), t E [0,1]. A pair of wavelets are constructed on the basis of Hermite cubic spline~: This wavelets are in C1 and supported on [0,2]. Moreover, one wavelet is symmetric, and the other is anti-symmetric. This spline wavelets are then adapted to the interval [0...

The present paper uses new approach and methodology to solve second order one dimensional hyperbolic telegraph equation numerically by B-spline collocation method. It is based on collocation of modified cubic B-spline basis functions over the finite elements. The given equation is decomposed into system of equations and modified cubic B-spline basis functions have been used for spatial variable...

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterraintegro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solutionis collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula.The error analysis of proposed numerical method is studied theoretically. Numerical results are given toil...

In this paper, the geometric interpolation of planar data points and boundary tangent directions by a cubic G2 Pythagorean-hodograph (PH) spline curve is studied. It is shown that such an interpolant exists under some natural assumptions on the data. The construction of the spline is based upon the solution of a tridiagonal system of nonlinear equations. The asymptotic approximation order 4 is ...

We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allows to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions ...

conclusions the use of smoothing methods helps us to eliminate non-linear effects but it is more appropriate to use cox proportional hazards model in medical data because of its’ ease of interpretation and capability of modeling both continuous and discrete covariates. also, cox proportional hazards model and smoothing methods analysis identified that age at diagnosis and tumor size were indepe...

The comprehensive numerical study has been made here for the solution of One dimensional heat equation the Finite Element method is adopted for the solution with B-spline basis function the important finding of the present study is to understand the basics behind the FEM method while the B-spline basis function come into the picture here the solution is made using Quadratic B-spline and Cubic B...

Shape preservation behavior of a spline consists of criterial conditions for preserving convexity, inflection, collinearity, torsion and coplanarity shapes of data polgonal arc. We present our results which acts as an improvement in the definitions of and provide geometrical insight into each of the above shape preservation criteria. We also investigate the effect of various results from the li...