Showing papers on "Function approximation published in 1977"
01 Jun 1977
TL;DR: The paper presents a method of numerically integrating a system of differential equations based on an idea of orthogonal approximation of functions that gives piecewise constant solutions with minimal mean-square error and is computationally similar to the familiar trapezoidal rule of integration.
Abstract: The paper presents a method of numerically integrating a system of differential equations based on an idea of orthogonal approximation of functions. Here, block-pulse functions are chosen as the orthogonal set. The method gives piecewise constant solutions with minimal mean-square error and is computationally similar to the familiar trapezoidal rule of integration. Design of piecewise constant controls or feedback gains for dynamic systems can be simplified following this approach.
160 citations
TL;DR: The method allows for the inclusion of additional information, such as uncertainties in the data and other constraints given by the general phenomenology of the experiment or theory, and can be applied to the calculation of numerical derivatives and integrals of data points.
67 citations
01 Nov 1977
TL;DR: In this article, an accurate approximation for calculating two-step diffusion profiles is given, valid for the field-free case has the same form as the Gaussian profile resulting from the conventional delta function approximation.
Abstract: An accurate approximation for calculating two-step diffusion profiles is given. The result valid for the field-free case has the same form as the Gaussian profile resulting from the conventional delta function approximation. The result is simple enough to be useful for first-order analytic evaluation of device fabrication parameters.
10 citations
TL;DR: In this article, an analytic model describing the transfer properties of a discrete photosensitive element position detection system is developed, which is shown to be possible to improve the inherently nonlinear transfer characteristic when the target is subject to perturbation in the form of Gaussian noise.
Abstract: An analytic model describing the transfer properties of a discrete photosensitive element position detection system is developed. Improvement of the inherently nonlinear transfer characteristic is shown to be possible when the target is subject to perturbation in the form of Gaussian noise. Applying a spline function approximation approach, relationship between the element threshold, noise variance, and element displacement are obtained which achieve the best (Chebyschev) approximation to an ideal (linear) transfer characteristic. Effective smoothing is shown to be obtainable for relatively small noise variance.
1 citations
01 Nov 1977
TL;DR: It is shown that the shape of the cross-correlation function of a nonlinear network consisting of the cascade connection of a linear network, a memoryless nonlinearity (NL) and a second linear network is independent, in the Gaussian case, of the presence of NL only when NL is not even.
Abstract: It is shown that the shape of the cross-correlation function of a nonlinear network consisting of the cascade connection of a linear network, a memoryless nonlinearity (NL) and a second linear network is independent, in the Gaussian case, of the presence of NL only when NL is not even. An explicit expression for the cross-correlation function of such a system is then given.
1 citations
01 Jan 1977
TL;DR: Techniques for estimating the accuracy and significance of approximations are given and several generalizations of Chebyshev series that lead to nearly best approximation with respect to almost arbitrary weight functions and basis sets are presented.
Abstract: Numerical analysis and approximation theory, in particular, can be an experimental science. This experimental nature is illustrated with several more-or-less new results. In the first half of this paper techniques for estimating the accuracy and significance of approximations are given. In the second half several generalizations of Chebyshev series that lead to nearly best approximations with respect to almost arbitrary weight functions and basis sets are presented.