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In computing, a roundoff error, [1] also called rounding error, [2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [3]
Stability is a measure of the sensitivity to rounding errors of a given numerical procedure; by contrast, the condition number of a function for a given problem indicates the inherent sensitivity of the function to small perturbations in its input and is independent of the implementation used to solve the problem. [5] [6]
This type of rounding, which is also named rounding to a logarithmic scale, is a variant of rounding to a specified power. Rounding on a logarithmic scale is accomplished by taking the log of the amount and doing normal rounding to the nearest value on the log scale. For example, resistors are supplied with preferred numbers on a logarithmic scale.
This could include rounding errors, or errors introduced by the measuring device. When σ² η is known we can compute the reliability ratio as λ = ( σ² x − σ² η) / σ² x and reduce the problem to the previous case. Estimation methods that do not assume knowledge of some of the parameters of the model, include
Finding an optimal solution to the above problem results in a quantizer sometimes called a MMSQE (minimum mean-square quantization error) solution, and the resulting PDF-optimized (non-uniform) quantizer is referred to as a Lloyd–Max quantizer, named after two people who independently developed iterative methods [6] [21] [22] to solve the two ...
Across the world, high-speed trains zip from city to city, sometimes topping 250 miles per hour before dropping off hundreds of passengers right in a city’s downtown. However, in the U.S., that ...
The field of numerical analysis predates the invention of modern computers by many centuries. Linear interpolation was already in use more than 2000 years ago. Many great mathematicians of the past were preoccupied by numerical analysis, [5] as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.
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