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Automatic differentiation and iterative processes [PDF]

Optimization Methods and Software, 1992
International audienceWe identify a class of iterative processes that can be used in the definition of a function while preserving the good behavior of automatic differentiation codes on this function.
Jean Charles Gilbert
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Iterative Weight Reduction Process

Journal of Ship Production and Design, 2018
In this article, iterative process for weight reduction was used by applying the design for manufacture and assembly process and FEM calculations. This study presents a successful development case of an oil sump structure of a large ship engine. Main structural modification was the transition from plate steel structures to sheet metal based panel ...
Tero Jokelainen, Antti Järvenpää, Kari Saine, Janne Tuominen, Kari Mäntyjärvi   +4 more
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The iterated Galton–Watson process

Journal of Applied Probability, 1996
We consider the mathematical properties of a time-discrete stochastic process describing explosive proliferation of DNA repeats in human genetic diseases. The process is constructed using a cascade of Galton–Watson branching processes. The main results concern the probability of absorption and the supergeometric growth of the process in the ...
Gawel, Boleslaw, Kimmel, Marek
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APP Relationship Calculation: An Iterative Process

IEEE Transactions on Knowledge and Data Engineering, 2015
Today, plenty of apps are released to enable users to make the best use of their cell phones. Facing the large amount of apps, app retrieval and app recommendation become important, since users can easily use them to acquire their desired apps. To obtain high-quality retrieval and recommending results, it needs to obtain the precise app relationship ...
Ming Liu 0004, Chong Wu 0001, Xiang-Nan Zhao, Chin-Yew Lin, Xiaolong Wang 0001   +4 more
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Laws of the iterated logarithm for iterated Wiener processes

Journal of Theoretical Probability, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hu, Y., Pierre-Loti-Viaud, D., Shi, Z.
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Iterative processes with „nucleolar“ restrictions

International Journal of Game Theory, 1977
Some aspects of the convergence of iterative processes are examined in a general context and a specific iterative process that generalizesStearns' K-transfer schemes is evolved. This yields a simplified proof ofStearns' convergence theorem and an iterative scheme that converges to the nucleolus.
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Derivative-Free Iteration Processes

SIAM Journal on Numerical Analysis, 1970
Zur iterativen Lösung der Fixpunktgieichung \(x=\Psi(x)\) im \(R^1\) werden in Verallgemeinerung des Steffensen-Verfahrens ableitungsfreie Verfahren höherer Ordnung entwickelt. Die Iterationsfunktion (Verfahren: \(y_{k+1}=\Phi(y_k), \quad k=0,1, \ldots \) ) hängt dabei rational von den Iterierten \(\Psi_0, \ldots, \Psi_n\) ab (Definition: \(\Psi_{0}(y)=
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Post‐processing of Gauss–Seidel iterations

Numerical Linear Algebra with Applications, 1999
The basic idea presented in the paper is backed by the convergence behaviour of a sequence of vectors \(x^k\) generated by an iterative method \(x^{k+1}=Bx^k+ c\), \(k=0,1,2,\dots \), solving a system \(Ax=b\) of \(n\) linear algebraic equations. It has been observed that the sequence \(\{x_i^{k+1}-x_i^k \}_{k=1}^\infty \), where \(i\) is a fixed index,
Michal Krízek, Liping Liu, Pekka Neittaanmäki   +2 more
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On the Continuous Realization of Iterative Processes

SIAM Review, 1988
The author gives a survey of continuous realization of several known basic iterative methods. A list of the presented methods is the following: Newton method, the steepest descent method, the QR algorithm, the power method, the SVD algorithm, the QZ algorithm and some linear stationary iterative method.
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Multifractality of nonlinear iterative processes

Journal of Statistical Physics, 1997
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