THE MAXIMUM AND MINIMUM OF A POSITIVE DEFINITE QUADRATIC POLYNOMIAL ON A SPHERE ARE CONVEX FUNCTIONS OF THE RADIUS

Abstract

It is proved that in Euclidean n-space the maximum M(rho) and minimum m(rho) of a fixed positive definite quadratic polynomial Q on spheres with fixed center are both convex functions of the radius rho of the sphere.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1969
Accession Number
AD0698800

Entities

People

  • George E. Forsythe

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Calculus
  • California
  • Computer Science
  • Computers
  • Differential Equations
  • Economic Development
  • Eigenvalues
  • Equations
  • Intervals
  • Military Research
  • Polynomials
  • Real Numbers
  • United States
  • United States Government
  • Universities

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Operations Research

Technology Areas

  • Space