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Division (mathematics)

About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.


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Patent
02 Nov 1989
TL;DR: In this paper, a multiplication, division and square root extraction apparatus which calculates the solutions to addition, division, and SE functions by approximation using iteration has a multiplier, an adder-subtracter and a shifter of prescribed bit width connected to a bus.
Abstract: A multiplication, division and square root extraction apparatus which calculates the solutions to addition, division and square root extraction functions by approximation using iteration has a multiplier, an adder-subtracter and a shifter of prescribed bit width connected to a bus. Iteration is conducted by inputting the output of the multiplier to the adder-subtracter or the shifter and returning the result to the input of the multiplier via the bus. A shifter and an arithmetic and logic unit connected to a second bus connected to the aforesaid bus via a switch have a greater bit width than the prescribed bit width and are used for large scale calculations, thus preventing a reduction in processing speed.

32 citations

Proceedings ArticleDOI
14 Jun 2006
TL;DR: In this article, a new asymptotically exact approach is presented for robust semidefinite programming, where coefficient matrices polynomially depend on uncertain parameters, and an approximate problem is constructed based on a division of the parameter region.
Abstract: A new asymptotically exact approach is presented for robust semidefinite programming, where coefficient matrices polynomially depend on uncertain parameters. Since a robust semidefinite programming problem is difficult to solve directly, an approximate problem is constructed based on a division of the parameter region. The optimal value of the approximate problem converges to that of the original problem as the resolution of the division becomes finer. An advantage of this approach is that an upper bound on the approximation error is available before solving the approximate problem. This bound shows how the approximation error depends on the resolution of the division. Furthermore, it leads to construction of an efficient division that attains small approximation error with low computational complexity. Numerical examples show efficacy of the present approach. In particular, an exact optimal value is often found with a division of finite resolution.

32 citations

Book ChapterDOI
25 Jun 2007
TL;DR: It is proved that this model characterises P and logspace uniform families are introduced, which characterises the power of a class of membrane systems that fall under the so-called P conjecture for membrane systems.
Abstract: In this paper we introduce a variant of membrane systems with elementary division and without charges. We allow only elementary division where the resulting membranes are identical; we refer to this using the biological term symmetric division. We prove that this model characterises P and introduce logspace uniform families. This result characterises the power of a class of membrane systems that fall under the so-called P conjecture for membrane systems.

32 citations

Proceedings ArticleDOI
25 Sep 2013
TL;DR: A typeclass in Haskell is defined for describing closed semirings, and a few functions for manipulating matrices and polynomials over them are implemented, which can be used to calculate transitive closures, find shortest or longest or widest paths in a graph, analyse the data flow of imperative programs, optimally pack knapsacks, and perform discrete event simulations.
Abstract: Describing a problem using classical linear algebra is a very well-known problem-solving technique. If your question can be formulated as a question about real or complex matrices, then the answer can often be found by standard techniques. It's less well-known that very similar techniques still apply where instead of real or complex numbers we have a closed semiring, which is a structure with some analogue of addition and multiplication that need not support subtraction or division. We define a typeclass in Haskell for describing closed semirings, and implement a few functions for manipulating matrices and polynomials over them. We then show how these functions can be used to calculate transitive closures, find shortest or longest or widest paths in a graph, analyse the data flow of imperative programs, optimally pack knapsacks, and perform discrete event simulations, all by just providing an appropriate underlying closed semiring.

31 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20242
2023739
20221,583
2021239
2020416
2019465