شماره ركورد كنفرانس :
4057
عنوان مقاله :
A version of the inverse function theorem for solving nonlinear equations
عنوان به زبان ديگر :
A version of the inverse function theorem for solving nonlinear equations
پديدآورندگان :
Anjidani Ehsan anjidani@neyshabur.ac.ir University of Neyshabur
كليدواژه :
Inverse function theorem , Nonlinear equation , Fr´echet derivative , Newton , type method.
عنوان كنفرانس :
چهارمين كنفرانس بين المللي آناليز غير خطي و بهينه سازي
چكيده فارسي :
The operator equation F(u) = h, where F is a nonlinear operator in a Hilbert space H is studied. Suppose that y is a
solution of F(u) = f. It is proved that the equation F(u) = h is uniquely solvable for any h in a sufficiently small neighborhood of
f, if F is Fr´echet differentiable on a neighborhood of y, F0 is continuous at y and F0(y) is invertible. The method of the proof is
similar to the proof of the inverse function theorem. Moreover, the convergence to the solution y by the Newton method
un+1 = un − [F0(u0)]−1(F(un) − f)
with an initial approximation u0, sufficiently close to y, is proved.
چكيده لاتين :
The operator equation F(u) = h, where F is a nonlinear operator in a Hilbert space H is studied. Suppose that y is a
solution of F(u) = f. It is proved that the equation F(u) = h is uniquely solvable for any h in a sufficiently small neighborhood of
f, if F is Fr´echet differentiable on a neighborhood of y, F0 is continuous at y and F0(y) is invertible. The method of the proof is
similar to the proof of the inverse function theorem. Moreover, the convergence to the solution y by the Newton method
un+1 = un − [F0(u0)]−1(F(un) − f)
with an initial approximation u0, sufficiently close to y, is proved.
