|
Extremum or
saddle point ?
Determines the nature of a stationary point —saddle point or
extremum—, for a certain kind of polynomial. |
|
|
| 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). |
