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991.
Junping Wang 《Numerische Mathematik》1989,55(4):401-430
Summary Asymptotic expansions for mixed finite element approximations of the second order elliptic problem are derived and Richardson extrapolation can be applied to increase the accuracy of the approximations. A new procedure, which is called the error corrected method, is presented as a further application of the asymptotic error expansion for the first order BDM approximation of the scalar field. The key point in deriving the asymptotic expansions for the error is an establishment ofL
1-error estimates for mixed finite element approximations for the regularized Green's functions. As another application of theL
1-error estimates for the regularized Green's functions, we shall present maximum norm error estimates for mixed finite element methods for second order elliptic problems. 相似文献
992.
A. Girard 《Numerische Mathematik》1989,56(1):1-23
Summary We propose a fast Monte-Carlo algorithm for calculating reliable estimates of the trace of the influence matrixA
involved in regularization of linear equations or data smoothing problems, where is the regularization or smoothing parameter. This general algorithm is simply as follows: i) generaten pseudo-random valuesw
1, ...,w
n
, from the standard normal distribution (wheren is the number of data points) and letw=(w
1, ...,w
n
)
T
, ii) compute the residual vectorw–A
w, iii) take the normalized inner-product (w
T
(w–A
w))/(w
T
w) as an approximation to (1/n)tr(I–A
). We show, both by theoretical bounds and by numerical simulations on some typical problems, that the expected relative precision of these estimates is very good whenn is large enough, and that they can be used in practice for the minimization with respect to of the well known Generalized Cross-Validation (GCV) function. This permits the use of the GCV method for choosing in any particular large-scale application, with only a similar amount of work as the standard residual method. Numerical applications of this procedure to optimal spline smoothing in one or two dimensions show its efficiency. 相似文献
993.
Wilhelm Heinrichs 《Numerische Mathematik》1989,56(1):25-41
Summary Spectral methods employ global polynomials for approximation. Hence they give very accurate approximations for smooth solutions. Unfortunately, for Dirichlet problems the matrices involved are dense and have condition numbers growing asO(N
4) for polynomials of degree N in each variable. We propose a new spectral method for the Helmholtz equation with a symmetric and sparse matrix whose condition number grows only asO(N
2). Certain algebraic spectral multigrid methods can be efficiently used for solving the resulting system. Numerical results are presented which show that we have probably found the most effective solver for spectral systems. 相似文献
994.
Stability regions of -methods for the linear delay differential test equations
0, \hfill \\ y(t) = \varphi (t),t \in [ - \tau ,0], \hfill \\ \end{gathered}$$
" align="middle" vspace="20%" border="0"> 相似文献
995.
Much recent work has been done to investigate convergence of modified continued fractions (MCF's), following the proof by Thron and Waadeland [35] in 1980 that a limit-periodic MCFK(a
n
, 1;x
1), with
andnth approximant
|