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The functional derivatives of the Rayleigh's quotient—concept and applications

✍ Scribed by J. Cioslowski


Publisher
John Wiley and Sons
Year
1987
Tongue
English
Weight
278 KB
Volume
32
Category
Article
ISSN
0020-7608

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Inequalities of Rayleigh quotients and b
✍ Don Coppersmith; Alan J. Hoffman; Uriel G. Rothblum 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 844 KB

Given a square, nonnegative, symmetric matrix A, the Rayleigh quotient of a nonnegative vector u under A is given by QA(u)= urAu//uru. We show that QA(~/u o Au ) is not less than QA(u), where ~--denotes coordinatewise square roots and o is the Hadamard product, but that QA(Au) may be smaller than QA