From e02b151999af3e2fdc74d302173000f562930cb6 Mon Sep 17 00:00:00 2001 From: Julian Weigt Date: Mon, 9 Feb 2026 22:31:37 +0100 Subject: Write some instructions. --- README.md | 10 +++++++++- 1 file changed, 9 insertions(+), 1 deletion(-) (limited to 'README.md') diff --git a/README.md b/README.md index f422ba8..a4ed6f1 100644 --- a/README.md +++ b/README.md @@ -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 Lp 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,∞}. -- cgit v1.2.3