Newton-Raphson method This method is based on the Newton-Raphson general algorithm for the solution of a set of simultaneous non-linear equations. F(X) = 0, where F is a vector of functions f1 to fn in variables x1, to xn. At each iteration of this method, the non-linear problem is...
Newton-Raphson methodNonlinear differential equationsA fast Newton-Raphson algorithm is developed for the finite-element solution of nonlinear boundary value problems. The linearized equation systems in the nonlinear iteration steps are solved by a block-preconditioned conjugate gradient...
Newton's method 1 Newton's method In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function. The algorithm is ...
We propose a new gradient--based method that mimics the Newton--Raphson method and makes use of both the gradient and the Hessian of the objective function. The proposed algorithm is designed to give guidance on how to choose the sequence of gains which plays a critical role in the ...
An algorithm for conical intersection optimization based on a double Newton-Raphson step (DNR) has been implemented and tested in 11 cases using CASSCF as the electronic structure method. The optimization is carried out in redundant coordinates, and the steps are the sum of two independent Newton...
raphsonanalysisstructuresmethodnewtonadaptive 1.INTRODUCTIONMaterialnonlinearanalysisisusedwhenthestiffnessofastructurechangesduetoyieldingofitsmembers;howevernonlinearanalysisprocedurehasnotbeenwidelyadoptedinpracticebecauseofthelargecomputationaleffortsandtechnicaldifficultiesinvolvedinthemodelingandanalysisprocedures.Howevertheneed...
Newton-Raphson method To find the roots x of a function f ( x ) in one dimension, given an initial guess x 0 , the Newton-Raphson method generates improvements using the iteration x i + 1 = x i − f ( x i ) / f ′ ( x i ) , where the dash denotes the derivative. The ...
Newton-Raphson methodThe precise positioning of a sea bottom transponder is very important for measuring the sea bottom crustal movement. In the previous ... H Isshiki - International Symposium on Underwater Technology 被引量: 5发表: 2004年 Acceleration of the Robust Newton Method by the Use of...
The preferred embodiment of the invention provides an improved apparatus for computing the reciprocal and reciprocal square root of an unknown value C using Newton's method. The improved method forms the reciprocal Newton iteration in the following two steps: ##EQU1## Each step requires only the...
Hence, in order to overcome this problem, we apply the Silver-Meal heuristic approach which produces a point as its starting point for the Newton-Raphson method to establish the steps of the algorithm. From the numerical examples, we show that the proposed method is more efficient than the ...