Results 261 to 270 of about 22,894 (307)
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BIT, 1985
In this expository paper the progress in factorization of large integers since the introduction of computers is reported. Thanks to theoretical advances and refinements, as well as to more powerful computers, the practical limit of integers possible to factor has been raised considerably during the past 20 years. The present practical limit is around \(
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In this expository paper the progress in factorization of large integers since the introduction of computers is reported. Thanks to theoretical advances and refinements, as well as to more powerful computers, the practical limit of integers possible to factor has been raised considerably during the past 20 years. The present practical limit is around \(
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Kernel-factorization deconvolution method
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1990zbMATH Open Web Interface contents unavailable due to conflicting licenses.
F. N. Kong, Z. P. Li
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Extension of the Factorization Method
Journal of Mathematical Physics, 1968We show that it is possible to extend the formalism of the factorization method for any displacement in the spectrum space of any second-order differential equation. Following this, we show that we can extend, at least formally, the formalism for some nth-order ordinary differential equations.
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A survey of spectral factorization methods
Numerical Linear Algebra with Applications, 2001AbstractSpectral factorization is a crucial step in the solution of linear quadratic estimation and control problems. It is no wonder that a variety of methods has been developed over the years for the computation of canonical spectral factors. This paper provides a survey of several of these methods with special emphasis on clarifying the connections ...
Ali H. Sayed, Thomas Kailath
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Turning Euler's Factoring Method into a Factoring Algorithm
Bulletin of the London Mathematical Society, 1996This paper presents an algorithm for factoring integers based on a factoring technique due to Euler. When factorization fails, the input is proved to be prime. Omitting details and special cases, the idea is to write an integer \(n\) in two ways: \(n=x^2_0+d\) and \(an= x^2_1+ dy^2_1\), where \(x_0, x_1, y_1, a,d\) are integers.
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Factoring Networks by a Statistical Method
Neural Computation, 1992We show that it is possible to factor a multilayered classification network with a large output layer into a number of smaller networks, where the product of the sizes of the output layers equals the size of the original output layer. No assumptions of statistical independence are required.
Nelson Morgan, Hervé Bourlard
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An efficient method for integer factorization
2015 IEEE International Symposium on Circuits and Systems (ISCAS), 2015In this paper, we propose an efficient method for integer factorization and it can be a good solution to sieving part of General Number Field Sieve. The mid-size integer factorization module adopts highly parallel structure to save operation time to a great extent.
Haibo Yu, Guoqiang Bai 0001
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Factorization and circuit in the connection method
Journal of the ACM, 1993Summary: A means of combining several search-space pruning rules, including factorization and circuit, into \textit{W. Bibel}'s connection method, is considered.
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Methods for transcription factor separation
Journal of Chromatography B, 2003Recent advances in the separation of transcription factors (TFs) are reviewed in this article. An overview of the transcription factor families and their structure is discussed and a computer analysis of their sequences reveals that while they do not differ from other proteins in molecular mass or isoelectric pH, they do differ from other proteins in ...
Robert A, Moxley +2 more
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On Integrating Factors and a Perturbation Method
Volume 3A: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration of Nonlinear, Random, and Time-Varying Systems, 1995Abstract In this paper the fundamental concept (due to Euler, 1734) of how to make a first order ordinary differential equation exact by means of integrating factors, is extended to n-th order (n ≥ 2) ordinary differential equations and to systems of first order ordinary differential equations.
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