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:
“I am not so foolish as to declaim against forms. Forms are as essential as bodies; but to exalt particular forms, to adhere to one form a moment after it is outgrown, is unreasonable, and it is alien to the spirit of Christ.”
—Ralph Waldo Emerson (1803–1882)
“I would urge that the yeast of education is the idea of excellence, and the idea of excellence comprises as many forms as there are individuals, each of whom develops his own image of excellence. The school must have as one of its principal functions the nurturing of images of excellence.”
—Jerome S. Bruner (20th century)