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When the errors on x are uncorrelated, the general expression simplifies to =, where = is the variance of k-th element of the x vector. Note that even though the errors on x may be uncorrelated, the errors on f are in general correlated; in other words, even if is a diagonal matrix, is in general a full matrix.
There are two major types of problems in uncertainty quantification: one is the forward propagation of uncertainty (where the various sources of uncertainty are propagated through the model to predict the overall uncertainty in the system response) and the other is the inverse assessment of model uncertainty and parameter uncertainty (where the ...
5.307 × 10 −10 – 8.349 × 10 −11 = 4.472 × 10 −10. This fraction is subtracted from 1 and multiplied by the pre-adjusted clock frequency of 10.23 MHz: (1 – 4.472 × 10 −10) × 10.23 = 10.22999999543. That is we need to slow the clocks down from 10.23 MHz to 10.22999999543 MHz in order to negate both time dilation effects.
n = 1 that yield a minimax approximation or bound for the closely related Q-function: Q(x) ≈ Q̃(x), Q(x) ≤ Q̃(x), or Q(x) ≥ Q̃(x) for x ≥ 0. The coefficients {(a n,b n)} N n = 1 for many variations of the exponential approximations and bounds up to N = 25 have been released to open access as a comprehensive dataset. [16]
The analysis of errors computed using the global positioning system is important for understanding how GPS works, and for knowing what magnitude errors should be expected. The Global Positioning System makes corrections for receiver clock errors and other effects but there are still residual errors which are not corrected.
This page was last edited on 3 June 2006, at 03:36 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply ...
Variable length arithmetic represents numbers as a string of digits of a variable's length limited only by the memory available. Variable-length arithmetic operations are considerably slower than fixed-length format floating-point instructions.
To illustrate, a simple example of this process is to find the mean and variance of the derived quantity z = x 2 where the measured quantity x is Normally distributed with mean μ and variance σ 2. The derived quantity z will have some new PDF, that can (sometimes) be found using the rules of probability calculus. [ 7 ]