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For example, an addition may produce an arithmetic overflow (it does not fulfill its contract of computing a good approximation to the mathematical sum); or a routine may fail to meet its postcondition. Exception: an abnormal event occurring during the execution of a routine (that routine is the "recipient" of the exception) during its execution.
Although this will not work in all cases, for example when calling the wrong subroutine, it is the easiest way to find the problem if the program uses the incorrect results of a bad mathematical calculation.
The second, usually called Truncation error, is the difference between the exact mathematical solution and the approximate solution obtained when simplifications are made to the mathematical equations to make them more amenable to calculation.
The question then is, whether there exists an algorithm that maps instances to solutions. For example, in the factoring problem, the instances are the integers n, and solutions are prime numbers p that are the nontrivial prime factors of n. An example of a computational problem without a solution is the Halting problem. Computational problems ...
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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]
Measurements generally have a small amount of error, and repeated measurements of the same item will generally result in slight differences in readings. These differences can be analyzed, and follow certain known mathematical and statistical properties.