Other Forms
In some nonlinear systems, parameters are explicit. In others they are implicit, and the system of nonlinear equations is written
where is an n-vector, and its image is an n-1 vector.
This formulation, without an explicit parameter space is not usually suitable for the formulations in the following sections, because they refer to parameterized autonomous nonlinear dynamical systems of the form:
However, in an algebraic system there is no distinction between unknowns and the parameters.
Read more about this topic: Numerical Continuation
Famous quotes containing the word forms:
“There are these sudden mobs of men,
These sudden clouds of faces and arms,
An immense suppression, freed,
These voices crying without knowing for what,
Except to be happy, without knowing how,
Imposing forms they cannot describe,
Requiring order beyond their speech.”
—Wallace Stevens (1879–1955)
“The delicious faces of children, the beauty of school-girls, “the sweet seriousness of sixteen,” the lofty air of well-born, well-bred boys, the passionate histories in the looks and manners of youth and early manhood, and the varied power in all that well-known company that escort us through life,—we know how these forms thrill, paralyze, provoke, inspire, and enlarge us.”
—Ralph Waldo Emerson (1803–1882)