Global monotone convergence of Newton-like iteration for a nonlinear eigen-problem
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The nonlinear eigen-problem Ax+F(x)=λ x is studied where A is an n× n irreducible Stieltjes matrix. Under certain conditions, this problem has a unique positive solution. We show that, starting from a multiple of the positive eigenvector of A, the Newton-like iteration for this problem converges monotonically. Numerical results illustrate the effectiveness of this Newton-like method.
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