Steepest descent and differential equations
نویسندگان
چکیده
منابع مشابه
Doubly Degenerate Diiusion Equations as Steepest Descent
For p 2 (1; 1) and n > 0 we consider the scalar doubly degenerate diiusion equation @ t s ? div(jrs n j p?2 rs n) = 0 in (0; 1) (1) with no{{ux boundary conditions. We argue that this evolution problem can be understood as steepest descent of the convex functional sign(m ? 1) Z s m ; provided m := n + p ? 2 p ? 1 > 0 ; (2) w. r. t. the Wasserstein metric of order p on the space of probability d...
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The steepest descent method has a rich history and is one of the simplest and best known methods for minimizing a function. While the method is not commonly used in practice due to its slow convergence rate, understanding the convergence properties of this method can lead to a better understanding of many of the more sophisticated optimization methods. Here, we give a short introduction and dis...
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Consider the following consistent Sylvester tensor equation[mathscr{X}times_1 A +mathscr{X}times_2 B+mathscr{X}times_3 C=mathscr{D},]where the matrices $A,B, C$ and the tensor $mathscr{D}$ are given and $mathscr{X}$ is the unknown tensor. The current paper concerns with examining a simple and neat framework for accelerating the speed of convergence of the gradient-based iterative algorithm and ...
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1Department of Mathematics, Shanghai Normal University, Shanghai; and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China 2Department of Mathematics & Statistics, College of Science, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia; and Department of Mathematics, Aligarh Muslim University, Aligarh, India 3Department of Applied Mathematics, National S...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1985
ISSN: 0025-5645
DOI: 10.2969/jmsj/03720187