Numerical Continuation - Continuation in More Than One Parameter

Continuation in More Than One Parameter

The parameter in the algorithms described above is a real scalar. Most physical and design problems generally have many more than one parameter. Higher dimensional continuation refers to the case when is a k-vector.

The same terminology applies. A regular solution is a solution at which the Jacobian is full rank . A singular solution is a solution at which the Jacobian is less than full rank.

A regular solution lies on a k-dimensional surface, which can be parameterized by a point in the tangent space (the null space of the Jacobian). This is again a straightforward application of the Implicit Function Theorem.