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The relation between local and global truncation errors is slightly different from in the simpler setting of one-step methods. For linear multistep methods, an additional concept called zero-stability is needed to explain the relation between local and global truncation errors.
Upload file; Search. Search. Appearance. Donate; ... Download as PDF; Printable version; ... Example A: Find the truncation in calculating the first derivative of () ...
Estimation of truncated regression models is usually done via parametric maximum likelihood method. More recently, various semi-parametric and non-parametric generalisation were proposed in the literature, e.g., based on the local least squares approach [5] or the local maximum likelihood approach, [6] which are kernel based methods.
Phase truncation spurs can be reduced substantially by the introduction of white gaussian noise prior to truncation. The so-called dither noise is summed into the lower W+1 bits of the PA output word to linearize the truncation operation. Often the improvement can be achieved without penalty because the DAC noise floor tends to dominate system ...
For example, consider the ordinary differential equation ′ = + The Euler method for solving this equation uses the finite difference quotient (+) ′ to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get (+) + (() +).
In the IEEE standard the base is binary, i.e. =, and normalization is used.The IEEE standard stores the sign, exponent, and significand in separate fields of a floating point word, each of which has a fixed width (number of bits).
The above definitions are particularly relevant in situations where truncation errors are not important. In other contexts, for instance when solving differential equations, a different definition of numerical stability is used. In numerical ordinary differential equations, various concepts of numerical stability exist, for instance A-stability.
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