|
Multidimensional
secant
Applies a multidimensional ("circular") secant method
to find a solution of a system of nonlinear equations. |
|
|
| n |
|
No. of variables and equations. • |
| c |
|
Coefficients in paraboloid (see below). • |
| a |
|
Constants in paraboloid. • |
Starting
values |
|
Starting values for the roots
(one
n-vector in each row). • |
| itmax, tol, monit |
|
Iterations (max.), tolerance
(≥ √εmach.), monitoring. • |
Applies a multidimensional "circular"
(i.e., one-at-a-time) secant method to find the solution
of a system of n nonlinear equations in n variables.
The base problem system is the gradient of a general paraboloid,
z = ∑i ci
(x − ai)2, with known solution,
x = a, a minimum (maximum), the coefficients, c,
being all positive (negative).
|
|
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| References: |
Plate: Msec081223 |
• Weisstein, Eric W., "Secant Method", from
MathWorld —a Wolfram Web Resource.
• Heath, Michael T.: one or several
nonlinear
equations.pdf
(=),
Lecture Notes
(CSciEng, UIUC).
• Walton,
Andrew G.: Solution
of nonlinear algebraic equations.pdf
(=),
Imperial College London.
• OTC
(Optimization Technology Center): Systems of nonlinear equations.
• Chemistry Dept.: CH 490/590,
Computer Programming for Scientists
(Oregon State Univ.).
• Conrad,
Eric van Fossen: Latin
phrases
(Ohio State Univ.).
• 1872-12-23: Pfeiffer, Georgii Yurii, born;
1722-12-23: Varignon, Pierre, died. |
