MAXIMIZING A SECOND-DEGREE POLYNOMIAL ON THE UNIT SPHERE

Abstract

Let A be a hermitian matrix of order n, and b a known vector in C(n). The problem is to determine which vectors make phi(x) = (x-b)(H)A(x-b) a maximum or minimum on the unit sphere U = (x : x(H)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 = O.

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Document Details

Document Type
Technical Report
Publication Date
Feb 05, 1965
Accession Number
AD0611427

Entities

People

  • Gene H. Golub
  • George E. Forsythe

Organizations

  • Stanford University

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Communities of Interest

  • Biomedical
  • Weapons Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Complex Numbers
  • Complex Variables
  • Computational Science
  • Computers
  • Differential Equations
  • Eigenvalues
  • Equations
  • Integral Equations
  • Mathematics
  • Military Research
  • Numbers
  • Numerical Analysis
  • Real Numbers
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  • United States

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Graph Algorithms and Convex Optimization.
  • Linear Algebra