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111.
第二类Fredholm积分方程的泰勒展开解法 总被引:3,自引:0,他引:3
本进一步发展了用Taylor公式求解第二类Fredholm积分方程的方法,并给出了近似解的误差精度分析. 相似文献
112.
113.
Enrique Bendito ngeles Carmona Andr s M. Encinas 《Applied Numerical Mathematics》2004,50(3-4):343-370
Our aim is to set the foundations of a discrete vectorial calculus on uniform n-dimensional grids, that can be easily reformulated on general irregular grids. As a key tool we first introduce the notion of tangent space to any grid node. Then we define the concepts of vector field, field of matrices and inner products on the space of grid functions and on the space of vector fields, mimicking the continuous setting. This allows us to obtain the discrete analogous of the basic first order differential operators, gradient and divergence, whose composition define the fundamental second order difference operator. As an application, we show that all difference schemes, with constant coefficients, for first and second order differential operators with constant coefficients can be seen as difference operators of the form
for suitable choices of q,
and
. In addition, we characterize special properties of the difference scheme, such as consistency, symmetry and positivity in terms of q,
and
. 相似文献
114.
115.
We propose a minimum mean absolute error linear interpolator (MMAELI), based on theL
1 approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation
for the coefficients of this linear functional is established in terms of the innovation series. It is found that information
implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations
following mixed normal andt distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI)
well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented.
Extensions to the general ARMA model and other time series models are discussed.
This research was supported by a CityU Research Grant and Natural Science Foundation of China. 相似文献
116.
Quantization consists in studying the L
r
-error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer(4) and Dereich et al.
(3) relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L
r
-quantization error from logarithmic small ball asymptotics and vice versa. 相似文献
117.
The presented work offers new algorithms for phase evaluation in interferometric measurements. Several phase-shifting algorithms with an arbitrary but constant phase-shift between captured intensity frames are proposed. These phase calculation algorithms need to measure five frames of the intensity of the interference field. The algorithms are similarly derived as so called Carré algorithm. The phase evaluation process then does not depend on the linear phase shift errors. Furthermore, the detailed analysis of the algorithms with respect to most important factors, which affect interferometric measurements, is carried out. It is also studied the dependency of the evaluation algorithms on the phase shift values, and the proposed phase calculation algorithms are compared with respect to the resulting phase errors. The influence of most important factors in the measurement and evaluation process was simulated as systematic and random errors using a proposed mathematical model. 相似文献
118.
119.
Francis J. Narcowich Joseph D. Ward Holger Wendland. 《Mathematics of Computation》2005,74(250):743-763
In this paper we discuss Sobolev bounds on functions that vanish at scattered points in a bounded, Lipschitz domain that satisfies a uniform interior cone condition. The Sobolev spaces involved may have fractional as well as integer order. We then apply these results to obtain estimates for continuous and discrete least squares surface fits via radial basis functions (RBFs). These estimates include situations in which the target function does not belong to the native space of the RBF.
120.