On some methods for entropy maximization and matrix scaling
نویسندگان
چکیده
منابع مشابه
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در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Lecture 1: Entropy, Convexity, and Matrix Scaling
Moreover, if p , q, then the inequality is strict. A proof: The map u 7→ −u log u is strictly concave on [0, 1]; this follows from the fact that its derivative −(1 + log u) is strictly decreasing on [0, 1]. Now, a sum of concave functions is concave, so we conclude that H is concave. Moreover, if p , q, then they differ in some coordinate; strict concavity of the map u 7→ −u log u applied to th...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1980
ISSN: 0024-3795
DOI: 10.1016/0024-3795(80)90171-8