## Quick Reference

*F*(*x*) = 0, let *x*^{(0)} be a first approximation to the solution. Let α be a parameter 0≤α≤1, then define the equations *F^*(*x*,α) = *F*(*x*) + (α-1)*F*(*x*^{(0)}) = 0 for α = 0, *x*^{(0)} is a solution; for α = 1, *F^*(*x*,1) = *F*(*x*) = 0, which are the original equations. Hence by solving the sequence of problems with α given by 0 = α_{0} < α_{1} < … < α* _{N}* = 1 the original problem is solved. As the calculation proceeds each solution can be used as a starting approximation in an iterative method for solving the next problem.

*F*(*x*) = 0,

*F^*(*x*,α) = *F*(*x*) + (α-1)*F*(*x*^{(0)}) = 0

*F^*(*x*,1) = *F*(*x*) = 0,

0 = α_{0} < α_{1} < … < α* _{N}* = 1

**From:**
continuation
in
A Dictionary of Computing »

*Subjects:*
Computing.