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SA

SA Solves a system of equations by successive approximation SA solves a system of equations by iterating on the evaluations of the equations: x[i] = x[i-1]+dx[i-1] until norm(f(x[i]))<=TolFun+RelTolFun*norm(f(x[0])), where dx = lambda*f(x). To enhance convergence SA uses a backtracking line search that divides dx by 2 until norm(f(x+dx)) decreases with respect to norm(f(x)) or until MaxSteps iterations have been done. X = SA(F,X0) tries to solve the system of equations F(X)=0 and start at the vector X0. F accepts a vector X and return a vector of equation values F evaluated at X. SA returns the vector X the root of F. X = SA(F,X0,OPTIONS) solves the problem using the options defined in the structure OPTIONS. Fields can be Display : 1 to display results of each iteration, 0 (default) if not lambda : adjustment parameter (default: 1) MaxIter : maximum number of iterations (default: 1000) MaxSteps : maximum number of backstepping iterations (default: 3) RelTolFun : relative convergence tolerance (default: sqrt(eps)) TolFun : absolute convergence tolerance (default: sqrt(eps)) X = SA(F,X0,OPTIONS,VARARGIN) provides additional arguments for F, which, in this case, takes the following form: F(X,VARARGIN). [X,FVAL] = SA(F,X0,...) returns the value of the equations F at X. [X,FVAL,EXITFLAG] = SA(F,X0,...) returns EXITFLAG that describes the exit conditions. Possible values listed below. 1 : SA converged to a root 0 : Failure to converge because of too many iterations or equations not defined at starting point