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Diffstat (limited to 'README.md')
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@@ -20,6 +20,14 @@ builds three files: - `charf_error` does computations using floating point (`double`) numbers and gives an upper bound for the total rounding error. - `charf_exact` does exact computations using fractions. Nominator and denominator are of type `unsigned long long` and bounded in size accordingly. +# Computation + +By default, the program goes through all possible characteristic functions on circles from length 2 to 36, considers derivatives from order 0 to 64 and exponents p = 1,2,4,8,∞. +Computing the maximal function of a function is the most computationally complex part. This means it is time efficient to consider several orders of derivative and exponents at the same time, in particular since the (k+1)th derivative is computed using the kth derivative. + +The program continuously outputs whenever it finds a function that beats the last record for the largest ratio of the L<sup>p</sup> norm of the kth derivative of the maximal function and the function. +It is also possible to print the results in human readable format and as a latex table. + # Correctness -I am relatively confident that the error bounds are correct for all operations except exponentiation, which is not used for p∈{1,∞}. +I am relatively confident that the computed error bounds are correct for all operations except exponentiation, which is not used for p∈{1,∞}. |