From f53272c1d31f37f07ff438f1e6d8e580a3649c83 Mon Sep 17 00:00:00 2001 From: julian-weigt Date: Sat, 11 Jul 2026 11:28:35 +0200 Subject: Use README formatting from Codeberg. --- README.md | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/README.md b/README.md index 576be51..f35620a 100644 --- a/README.md +++ b/README.md @@ -1,6 +1,8 @@ +# discrete-mf + For functions f on the discrete circle {0,…,N-1} this program computes their uncentered maximal functions and the ratio of the Lp norms of the kth derivative of the maximal function and the function. -# Building +## Building If `git` is installed you can fetch the repository using @@ -20,7 +22,7 @@ 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 +## Computation By default, the program goes through all 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. @@ -28,7 +30,7 @@ Computing the maximal function of a function is the most computationally complex 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. -# Error bounds +## Error bounds Even for a characteristic function that only take values 0 or 1, its maximal function may not be integer valued. The most widespread way to do non integer arithmetic on a computer is floating point arithmetic. This however is not exact, so results cannot be trusted a priori. This program implements two alternative ways to make results reliable: -- cgit v1.3