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Extremum or saddle point ?
  Determines the nature of a stationary point —saddle point or extremum—, for a certain kind of polynomial.
2024.Nov.25 03:36:33
n, npar No. of independent variables and parameters [npar = n (n + 3) ⁄ 2 + 1]. •
A A-values given as a0, a1..n, a1,1..n (see below).
  Determines the nature of a stationary point (null first derivatives) for a polynomial: an extremum or a saddle point. Sufficient conditions are sought to classify the point. Only up to second order terms are considered (in spite of following).
  The coefficients must be given in the order a0, a1..n, ai,j..n, i = 1..n, j = i..n. Thus, for n = 4, it is:
a0; a1, a2, a3, a4; a11, a12, a13, a14, a22, a23, a24, a33, a34, a44.
References or suggested reading:

• Finney, R. L., G. B. Thomas, Jr., M. D. Weir, 1994, “Thomas’ Calculus”, Addison-Wesley; G. B. Thomas, R. L. Finney, M. D. Weir, F. R. Giordano, 2001, —, 10.th ed..

• Pike, Ralph W., 2001, “Optimization for Engineering Systems”, Louisiana State University (table of contents).

 
 
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Created: 2005-06-09 — Last modified: 2007-11-28