Lower bounds for multivariate approximation by affine-invariantdictionaries

The problem of approximating locally smooth multivariate functions by linear combinations of elements from an affine-invariant redundant dictionary is considered. Augmenting previous upper bound results for approximation, we establish lower bounds on the performance of such schemes. The lower bounds are tight to within a logarithmic factor in the number of elements used in the approximation. Using a previously introduced notion of nonlinear approximation, we show that the approximation ability may be completely characterized by the pseudodimension of the approximation space with respect to a finite set of points. This result establishes a useful link between the problems of approximation and estimation, or learning, the latter often being conveniently characterized, at least in terms of upper bounds, by the pseudodimension     

Approximation for the Two‐Dimensional Gaussian Q‐Function and Its Applications

In this letter, we present a new approximation for the two‐dimensional (2‐D) Gaussian Q‐function. The result is represented by only the one‐dimensional (1‐D) Gaussian Q‐function. Unlike the previous 1‐D Gaussian‐type approximation, the presented approximation can be applied to compute the 2‐D Gaussian Q‐function with large correlations.     

Simplified Green's function for SAW generation which allows for the LSW

An approximation for the Green's function used to analyse surface-acoustic-wave generation on piezoelectrics is proposed. It allows for the effect of the leaky surface wave. The result is useful for calculating the reflectivity of, and velocity change due to, thin metal dots on Y-cut LiNbO3.     

The small slope approximation reflection coefficient for scatteringfrom a “Pierson-Moskowitz” sea surface

First- and second-order reflection coefficients are presented for the small slope approximation. The first-order reflection coefficient is identical to the Kirchhoff, or physical optics, result, and the second-order reflection coefficient reduces to those of perturbation theory and the Kirchhoff approximation in the appropriate limits. Numerical results are obtained for acoustic or TE-polarized electromagnetic scattering from one-dimensional, “Pierson-Moskowitz” sea surfaces at low grazing angles. Comparison with exact integral equation results shows that the second-order small slope approximation is extremely accurate and better than both the perturbation and Kirchhoff methods     

一种非均匀掺杂的全耗尽SOI-MOSFET阈值电压模型

对垂直于沟道的二维电势分布函数提出了一种新的近似,给出了基于这种近似的杂质浓度呈高斯分布的非均匀掺杂全耗尽SOI-MOSFET的阈值电压解析模型.模型结果与MEDICI数值模拟结果符合得很好,表明了模型的准确性,这为实践中分析与控制非均匀掺杂的全耗尽SOI-MOSFET的阈值电压提供了一种新的途径.     

一种非均匀掺杂的全耗尽SOI-MOSFET阈值电压模型(英文)

对垂直于沟道的二维电势分布函数提出了一种新的近似,给出了基于这种近似的杂质浓度呈高斯分布的非均匀掺杂全耗尽SOI-MOSFET的阈值电压解析模型.模型结果与MEDICI数值模拟结果符合得很好,表明了模型的准确性,这为实践中分析与控制非均匀掺杂的全耗尽SOI-MOSFET的阈值电压提供了一种新的途径.     

一种非均匀掺杂的全耗尽SOI-MOSFET阈值电压模型

对垂直于沟道的二维电势分布函数提出了一种新的近似,给出了基于这种近似的杂质浓度呈高斯分布的非均匀掺杂全耗尽SOI-MOSFET的阈值电压解析模型.模型结果与MEDICI数值模拟结果符合得很好,表明了模型的准确性,这为实践中分析与控制非均匀掺杂的全耗尽SOI-MOSFET的阈值电压提供了一种新的途径.     

Closed-form solution for underground impedance calculations

Recently, a closed-form solution for the self-impedance of a conductor directly buried in the earth has been conjectured through analogy with other closed-form approximations for overhead conductors. This letter provides a mathematical development for the equation and extends the results to the more general case of a conductor contained in a dielectric tunnel deep within a medium of arbitrary relative permeability. The derivation shows the mathematical approximations which are needed in obtaining the desired result and introduces a new simple, yet surprisingly accurate approximation for the ratio of Kelvin functions which is superior to the one-term approximation currently in use.     

An approximation for the phase offset sensitivity of Viterbidetected continuous phase modulation signals

An approximation is presented for the loss in performance when the Viterbi algorithm receiver for CPM (continuous phase modulation) signals is subject to a phase offset. Pairs of symmetric error events are used to derive a closed-form result that approaches the asymptotic expression, based solely on minimum distance, as E_s/ N₀ approaches infinity. The improved accuracy of the approximation is demonstrated by comparison with a Monte Carlo simulation     

Multiuser detection for square-law receiver under Gaussian channel noise with applications to fiber-optic communications

In fiber-optic wavelength-division multiplexing (WDM) communications systems, the nonlinearity of the channel and the limitations of optical filters result in received channel signals that are correlated. Furthermore, the square-law nature of the detector converts the additive fiber amplifier noise to a data-dependent asymmetric and non-Gaussian noise. The optimal multiuser detector for a Gaussian approximation is compared to the actual statistics and found to give a close performance estimate. Through bounds on the error probability and the asymptotic multiuser efficiency, the optimal multiuser detector based on a Gaussian approximation is found to improve significantly performance in highly correlated data cases. This result is applied to a practical optical WDM system.     

Eikonal equation for moving media and its relation to dynamic programming

The eikonal equation for moving media (first order in V/c) is derived for the electromagnetic case. Maxwell's equations with Minkowski's constitutive relations, and the dynamic programming approach, lead to essentially the same result. The acoustical eikonal equation for moving media is derived by means of the dynamic programming method. A result obtained by Kritikos, believed to be wrong, is shown to be valid as an approximation.     

Coupling factor for 0° asymmetric nonuniform line couplers

The phase difference between the coupled outputs is calculated in a 2nd-order approximation for asymmetric nonuniform line couplers. This result permits one to propose an even-mode characteristic-impedance variation for the design of a 0° coupler, which is more easily computable than the Klopfenstein taper previously used.     

Approximation of multivariable functions by M-D transfer functions with separable denominator

The approximation of a given function by a rational function has been considered extensively by mathematicians. A particular result has been stated by Walsh that the best approximation of a given analytical function is one which interpolates the given function at several properly chosen points. In this paper, transfer functions of multidimensional digital filters with separable denominator are used for the approximation of given multivariate functions. It is shown that the result of Walsh can be generalized in a straightforward manner. By an example it is illustrated how the new result can be applied to, e.g., the order reduction of a higher-order system. In the conclusion we state the usefulness and the limitation of the result.     

Adaptable,Fast, Area-Efficient Architecture for Logarithm Approximation with Arbitrary Accuracy on FPGA

This paper presents ALA (Adaptable Logarithm Approximation), a novel hardware architecture for the approximation of the base-2 logarithm of integers at an arbitrary accuracy, suitable for fast and area-efficient FPGA implementation. It is based on a piecewise linear approximation methodology, implemented so that an arbitrary number of linear segments approximate the logarithm function. The achieved approximation accuracy depends on the number of segments used, which also affects the size of a ROM used for storing the parameters that control the computation. The implementation of the ROM using an FPGA BlockRAM allows the parameters to be updated without reconfiguration of the FPGA core. This provides the considerable advantage of data set adaptability to the proposed architecture over the other relevant architectures, as the parameters can be easily updated to minimize the approximation error for different data sets. Both real and synthetic datasets have been used for evaluation purposes. The results show that ALA adapts well to all data sets used and requires significantly less FPGA slices than the CORDIC architecture to achieve the same or higher approximation accuracy. Moreover, it provides a throughput of one result per cycle and up to four times lower latency than the CORDIC core.     

On the far-field approximation for scattering from randomly rough surfaces

Various authors have justified the far-fields approximation for rough surface scattering using one of the classical approximations for the scattered fields, usually considering either the coherent scattered field or the incoherent scattered intensity. An exact expression for the field scattered from a perfectly conducting rough surface is considered. The expression for the incoherent scattered intensity is formally derived, and a condition under which the far-field approximation is valid is found, independent of specific approximations for the surface or scattered fields or for the surface height statistics. The condition so derived is, under many circumstances, substantially less restrictive than that derived before in the general case. Furthermore, the previous results may be easily recovered by further specialization of our result.     

Performance analysis for hierarchical multirate loss networks

The reduced load approximation technique has been extensively applied to flat networks, but the feasibility of applying it to hierarchical network model has seldom been described. Hierarchical routing is essential for large networks such as the Internet inter/intra-domain routing hierarchy and the Private Network to Node Interface (PNNI) standard. Therefore, this paper proposes an efficient and accurate analytical model for evaluating the performance of hierarchical networks with multiple classes of traffic. A performance analysis model with considering multiple classes of traffic, the complexity of analytical and explosion of computation will be extremely increased, and hence, result in inaccurate analytical. The issue of multiple classes of traffic has to be addressed in performance analysis model. In this paper, we first study the reduced load approximation model for loss networks, and then propose a novel performance evaluation model for large networks with multirate hierarchical routing. The hierarchical evaluation model is based on decomposing a hierarchical route into several analytic hierarchical segments. Once the blockings of these hierarchical segments are accurately determined, the blocking of the hierarchical path can be estimated accurately from these segments blocking. Numerical results indicate that the proposed hierarchical reduced load approximation yields quite accurate blocking probabilities as compared to that of simulation results. Furthermore, the accuracy of the proposed hierarchical reduced load approximation heuristic is independent of the blocking or the offered traffic load. Finally, we also draw some remarks on the convergence of the reduced load based approximation analysis model.     

Queueing performance estimation for general multifractal traffic

We present an approximation for the tail asymptotics in an infinite capacity single server queue serviced at a constant rate driven by general multifractal input process. We show that in the special and important case of the monofractal fractional Brownian motion input traffic our result gives the well‐known Weibullian tail. We prove that the class of Gaussian processes with scaling properties is in the class of monofractal processes and we derive the related characterization functions. Our formula in the case of Gaussian input processes also gives a queueing result which is in good agreement with the theory of Gaussian processes. Applying the approximation we provide a new practical method for queueing performance estimation of general multifractal traffic. The validation of the method based on both analysis of simulations and measured network traffic have also been presented. Copyright © 2003 John Wiley & Sons, Ltd.     

Accurate metallization capacitances for integrated circuits and packages

The parallel-plate formula is widely used by the solid-state circuit designer to estimate capacitances in integrated circuits. Since considerable errors may result from using this approximation, this correspondence gives correction curves for a wide range of parameters. It is shown that the finite conductor thickness may significantly contribute to the increase in capacitance.     

Error estimation for numerical differential equations

Given a capable human being and a computer, it is possible to make an approximation to the solution of a nonlinear differential equation. However, under the (usually correct) assumption that the equation is analytically intractable, the result of the computation is not the exact solution; indeed it may be so far from the exact solution as to be completely useless. We are interested in the relationship between the effort expended by the human and the computer, and the duality of the computed approximation to a partial or ordinary differential equation. To be specific, we would like to think in terms of a cost-benefit analysis. The cost of the computation is a combination of the human effort and computer resources used to obtain the approximation. The benefit includes, of course, the computed approximation, but it also includes an estimate of the quality of the approximation, that is, an error estimate. It is our opinion that in computational science, as with the experimental sciences, results should always be presented with some estimate of their accuracy. In addition, however, there is another facet to error estimation: one cannot even attempt a cost-benefit analysis or efficiency comparison of methods without an error estimate to evaluate the results     

专用DSP中的特殊运算单元的设计及实现

介绍了一种称为GDSP的针对多协议处理的16位定点专用DSP,它具有一条指令完成取双操作数、运算及结果写回memory的特点,针对算法特点设计的三角函数运算单元CDC、二进制对数/指数运算的算法改进及VLSI实现的对数运算单元LOG和指数运算单元ANTILOG,能快速精确的完成三角函数和对数/指数的求解。该DSP系统在保证精度的同时,具有强大的运算能力。