𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Online computations of differentiable functions

✍ Scribed by Matthias Schröder

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
854 KB
Volume
219
Category
Article
ISSN
0304-3975

No coin nor oath required. For personal study only.

✦ Synopsis

We show that Lipschitz-continuously differentiable functions f : ([-I; I])k + R which are computable in time I'( T(n)), where T is regular, can be computed online in time C'( T(n) + .&(n) log(n)) on a Type-2-machine, where .I:n~n log(n) log log(n) is the Schiinhage-Strassenbound for integer multiplication and n refers to the desired output precision (f )". Online computation means that for determining the nth output digit to the right of the binary point the algorithm only requires the first n + 6 digits of the input reals, where 6 is a constant called the delay of the algorithm.

📜 SIMILAR VOLUMES

On the complexity of online computations
On the complexity of online computations of real functions
✍ Klaus Weihrauch 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 813 KB

A reasonable computational complexity theory for real functions is obtained by using the modified infinite binary representation with digits 0, 1, and -1 for the real numbers and Turing machines which transform with one-way output modified binary input sequences into modified binary output sequences

Differentiable functions of quaternion v
Differentiable functions of quaternion variables
✍ S.V. Lüdkovsky; F. van Oystaeyen 📂 Article 📅 2003 🏛 Elsevier Science 🌐 French ⚖ 391 KB

We investigate differentiability of functions defined on regions of the real quaternion field and obtain a noncommutative version of the Cauchy-Riemann conditions. Then we study the noncommutative analog of the Cauchy integral as well as criteria for functions of a quternion variable to be analytic.

Construction of differentiable membershi
Construction of differentiable membership functions
✍ A. Grauel; L.A. Ludwig 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 405 KB

In many applications of fuzzy logic it is of special interest to have a transfer function with good properties regarding differentiability. To that end it is desirable to have continuously differentiable membership functions with only few parameters. In this paper we propose a class of symmetrical a