A choice of norm in discrete approximation ∗
نویسندگان
چکیده
We consider the problem of choice of norms in discrete approximation. First, we describe properties of the standard l1, l2 and l∞ norms, and their essential characteristics for using as error criteria in discrete approximation. After that, we mention the possibility of applications of the so-called total least squares and total least lp norm, for finding the best approximation. Finally, we take a look at some nonstandard, visual error criteria for qualitative smoothing.
منابع مشابه
Continuous Discrete Variable Optimization of Structures Using Approximation Methods
Optimum design of structures is achieved while the design variables are continuous and discrete. To reduce the computational work involved in the optimization process, all the functions that are expensive to evaluate, are approximated. To approximate these functions, a semi quadratic function is employed. Only the diagonal terms of the Hessian matrix are used and these elements are estimated fr...
متن کاملFuzzy Best Simultaneous Approximation of a Finite Numbers of Functions
Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.
متن کاملCalculation of the Induced Charge Distribution on the Surface of a Metallic Nanoparticle Due to an Oscillating Dipole Using Discrete Dipole Approximation method
In this paper, the interaction between an oscillating dipole moment and a Silver nanoparticle has been studied. Our calculations are based on Mie scattering theory and discrete dipole approximation(DDA) method.At first, the resonance frequency due to excitingthe localized surface plasmons has been obtained using Mie scattering theory and then by exciting a dipole moment in theclose proximity of...
متن کاملA continuous approximation fitting to the discrete distributions using ODE
The probability density functions fitting to the discrete probability functions has always been needed, and very important. This paper is fitting the continuous curves which are probability density functions to the binomial probability functions, negative binomial geometrics, poisson and hypergeometric. The main key in these fittings is the use of the derivative concept and common differential ...
متن کاملA Two Level Approximation Technique for Structural Optimization
This work presents a method for optimum design of structures, where the design variables can he considered as Continuous or discrete. The variables are chosen as sizing variables as well as coordinates of joints. The main idea is to reduce the number of structural analyses and the overal cost of optimization. In each design cycle, first the structural response quantities such as forces, displac...
متن کامل