| Case
|
Algorithm
|
| Polynomial root finding
|
The Jenkins-Traub algorithm is used.
|
| Solving sparse linear systems
|
This solver is based on Gauss factoring with Markowitz products.
|
| Solving other linear equations
|
Gaussian elimination and other methods of linear algebra are used.
|
| Solving systems of algebraic equations
|
Numerical Gröbner basis using an efficient monomial
ordering and then eigenvalue methods to extract numerical roots are used.
|
| Solving polynomial equations up to degree four
|
Explicit formulas are used.
|
| Solving polynomial equations above degree four
|
Polynomials are reduced using factoring and decomposition, and
cyclotomic and other special polynomials are recognized.
|
| Solving systems of polynomial equations
|
Gröbner basis using an efficient version of the
Buchberger algorithm is used.
|
| Solving nonpolynomial equations
|
This solver uses change of variables with the addition
of polynomial side conditions.
|
| Function minimization of sum of squares
|
The Levenberg-Marquardt method is used.
|
| Function minimization in one dimension
|
This solver uses Brent's conjugate gradient method.
|
| Function minimization in more than one dimension
|
A modification of Powell's method is used.
|
| Root finding
|
There is an automatic choice between damped Newton's method, the secant
method, and Brent's method.
|
| Numeric ordinary differential equation and partial
differential equation solving
|
This solver switches automatically between a nonstiff Adams method and
a stiff Gear method and is based on LSODE.
|
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