Parametric Spatial Basis Functions and Approximations
Parameter optimization of orthonormal basis functions for efficient rational approximations
... Table 1: Comparison of relative errors The second example deals with an infinite dimensional function. This is a far more complex issue. Classical MOR methods that only apply to rational original models are not suitable ...
18
A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation
... represent parametric curves and ...ing functions can be seen as a generalization of the polynomial Keys interpolator to higher orders as well as its extension with respect to the reproduction of exponential ...
11
A family of smooth and interpolatory basis functions for parametric curve and surface representation
... represent parametric curves and ...ing functions can be seen as a generalization of the polynomial Keys interpolator to higher orders as well as its extension with respect to the reproduction of exponential ...
11
Stable Computations with Flat Radial Basis Functions Using Vector-Valued Rational Approximations
... radial basis functions (RBFs) that scaling the kernels so they are ‘flat’ leads to smaller discretization ...analytic functions with the property that all components of the vector share the same ...
27
basis functions
... Quoc Thong Le Gia 1 William McLean 2 (Received 27 January 2011; revised 20 April 2011) Abstract We propose a method to construct numerical solutions of a parabolic equation on the unit sphere. The time discretisation ...
14
A numerical study of compact approximations based on flat integrated radial basis functions for second-order differential equations
... In this paper, we propose a simple but effective preconditioning technique to im- prove the numerical stability of Integrated Radial Basis Function (IRBF) meth- ods. The proposed preconditioner is simply the ...
36
Non-Parametric Spatial Models
... covariance functions are not applicable for such ...underlying spatial processes while retaining most of the ...tapering functions are often chosen from stationary correlation functions for ...
101
Non-parametric and semi-parametric estimation of spatial covariance function
... symmetric spatial random fields on sphere with a kernel convolution ...kernel functions. By allowing the parameters in the kernel functions to vary with locations, we are able to generate a flexible ...
101
Markov chain approximations to scale functions of Lévy processes
... elementary/special functions, and less often still is it possible to obtain closed-form expressions for W ...a parametric complex integral of the L´evy measure, making it hard to discern how a perturbation ...
26
Triangular approximations of fuzzy number with value and ambiguity functions
... I n some applications of fuzzy logic, it is difficult to use general fuzzy numbers therefore, it may be bet- ter to use fuzzy numbers with the same type. Some re- searchers introduce the defuzzification method which ...
5
Radial Basis Function Finite Difference Approximations of the Laplace-Beltrami Operator
... Finite difference methods are a common and effective technique for numerically solving PDEs. These methods involve finding approximate solutions at discrete points on uniform spatial grids. Therefore, they are ...
92
Modeling spatial covariance functions
... the spatial data analysis as it provides important information about the dependence structure of underlying processes and determines performance of spatial ...Various parametric models have been ...
84
2 Functions and approximations
... The following section introduces some of the most common methods, such as Taylor expansions and finite differences, for approximating functions and provides some tips and tricks for using graphing and plots to ...
10
Topological Approximations for Spatial Representations
... Synthetic perception of architectural space is potentially a powerful concept. Besides the speed and the accuracy, it could help us explicitly define essential design parameters, and critically assess our own methods of ...
25
Better approximations to cumulative normal functions
... rational functions to obtain the approxima- ...these functions (‘f relative to g’ at a point x means that we are graphing the value f (x) g(x) −g(x) ...the functions involved are symmetric, we only ...
7
Legendre Wavelet expansion of functions and their Approximations
... Abstract In this paper, nine new Legendre wavelet estimators of functions having bounded third and fourth derivatives have been obtained.These estimators are new and best approximation in wavelet analysis. ...
25
Piecewise-Linear Approximations of Multidimensional Functions
... Linear interpolation between fixed gridpoints can also be used to approximate generic, nonlinear functions, allowing us to approximately solve problems using linear, rather than nonlinear, programming techniques. ...
31
Algorithms for the computation of approximations by algebraic functions
... The main results established were that a clear formulation of the approximation problem leads to the existence of a unique approximating algebraic form which determines the [r] ...
13
Parametric, Vector, and Polar Functions
... We can then identify each point P in the plane by polar coordinates ( r , ), where r gives the directed distance from O to P and gives the directed angle from the initial ray to th[r] ...
32