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  error estimate
Stability in l-norm and error estimate in I2-norm are obtained.
      
By using the elliptic Ritz-Volterra projection, the analysis of the error estimates for the finite element numerical solutions and the optimal H1-norm error estimate are demonstrated.
      
Calculation of maximum value of twice-differentiable function with a posteriori error estimate
      
An error estimate is derived, and an a priori choice of the regularization parameters is described.
      
An error estimate is obtained for the stable approximate solution obtained by solving a set of linear algebraic equations for the wavelet coefficients of the desired solution.
      
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  error estimates
In this paper, we prove the convergence of the nodal expansion method, a new numerical method for partial differential equations and provide the error estimates of approximation solution.
      
Furtheremore, we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.
      
The ellipticH2-Volterra projection is induced and then used in the derivations of error estimates for semi-discrete and full-discreteH1-Galerkin methods.
      
The optimalL2,H1 andH2 norm error estimates are obtained.
      
Continuous time and discrete time Galerkin methods are introduced to approximate the solution and optimalH1 error estimates are obtained.
      
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  error estimation
The large time error estimation between the spectral approximate solution and the exact solution is obtained.
      
Phase-shifting measurement and its error estimation method were studied according to the holographic principle.
      
The difficulties of the error estimation in phase-shifting phase measurement were restricted by this error estimation method.
      
Meanwhile, the maximum error estimation method of phase-shifting phase measurement and its formula were proposed.
      
A formula is presented for the approximate calculation of the correlation coefficient with error estimation.
      
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  estimation of error
Consistent nonparametric estimation of error distributions in linear model
      
The existence and uniqueness theorem of its solution is proved by the perturbation method and the estimation of error for its approximate solution is given.
      
Estimation of error variance in one-way random model
      
The criterion used is the estimation of error variance.
      
We investigated the correlation coefficient (r) and standard estimation of error (SEE) between the latter ten static images and the DV image using the pixel-by-pixel method, thereby determining the optimum acquisition phase.
      
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The experimental data processing method of measuring the mean-free-path of nuclear in-teractions is discussed.Estimator formulas in several experimental conditions are obtained byusing the maximum likelihood method.The result of Mente-Carlo simulation shows that in caseof the experimental data with poor statistics the maximum likelihood estimate value is more ac-curate than the least squares fitting value geuerally used

本文讨论了测定核作用平均自由程的实验中的数据处理方法.采用最大似然法得出了几种不同实验情况下核作用平均自由程的估计式及其标准误差估计式.蒙特卡洛模拟的结果表明,在统计量不大的情况下,最大似然估计值比常用的最小二乘拟合值更精确.

The error estimation formula for numerical calculation of wave optics MTF has been derived with mathematical statistics method. It is suitable for error estimation of MTF values obtained from different numerical computational methods, which are used for the self-correlation integrating. Based on the fundamental property of wave optics, a new numerical computational method for MTF was developed. This method not only hag higher numerical accuracy but also can reduce the computational amount in great deal

用数理统计方法,推导出波动光学MTF数值计算的误差估计式,它适用于对不同的数值计算方法进行自相关积分所求得的MTF值进行误差估计.本文根据波动光学的基本性质,提出了新的MTF数值计算方法,它具有较高的数值精度,更可观的计算量大大减少.

A system composed of a seismic profiler and a hydrophone streamer towed behind the profiler has been considered for acoustic velocity measurements of sea-bed sediment layers. It is indicated that the T2-X2 approach with Common-Depth-Point processing is the basic way to measure acoustic velocities of arbitrarily dipped layers. Based on Shah's ray-tracing formulation, equations for velocity computations of the layers below sea-bottom are derived and procedures to solve them explained. Through the analysis of errors...

A system composed of a seismic profiler and a hydrophone streamer towed behind the profiler has been considered for acoustic velocity measurements of sea-bed sediment layers. It is indicated that the T2-X2 approach with Common-Depth-Point processing is the basic way to measure acoustic velocities of arbitrarily dipped layers. Based on Shah's ray-tracing formulation, equations for velocity computations of the layers below sea-bottom are derived and procedures to solve them explained. Through the analysis of errors in measuring velocities, which are caused by deviation of the time-distance curve from an ideal hyperbola, instability of towing speed, echo-time jitters and streamer declination, the problem of determining the major parameters of the measurement system is clarified.

海底地层声速的测量系统由地层剖面仪加一条拖曳水听器阵组成。在地层界面为任意倾斜的情况下,按照T~2-X~2法的原理对共深度点的回波数据进行计算是测量地层声速的基本方法。根据地层声速和阵移速度之间关系的一般表达式,结合对各界面的正射线的几何分析,导出了计算海底下各层声速的方程式,并且讨论了用简便的迭代法求解这些方程式的有关问题。用T~2-X~2法测量声速的误差主要来源于:回波时距曲线偏离理想的双曲线,水听器阵拖曳速度不稳定和回波到达时间的随机漂移。通过分析,得到了相应的误差估计公式。由此,也为正确决定测量系统的设计参数提供了依据。

 
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