MAXIMIZING A SECOND-DEGREE POLYNOMIAL ON THE UNIT SPHERE BY GEORGE E. FORSYTHE and GENE H. GOLUB
نویسنده
چکیده
Let A be a hermitian matrix of order n, and b a known vector n H in C . The problem is to determine which vectors make ^(x) = (x-b) A(x-b) H a maximum or minimum on the unit sphere U = fx : x x = 1} . The problem is reduced to the determination of a finite point set, the spectrum of (A,b). The theory reduces to the usual theory of hermitian forms when b = 0. *J Reproduction in Whole or in Part is Permitted for any Purpose of the United States Government. This report was supported in part by Office of Naval Research Contract Nonr-2?5 (',? ) (NR-0U1+-21J ) at Stanford University.
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