Kepler equation and accelerated Newton method

Accelerated Regularized Newton Method for Unconstrained Convex Optimization∗

We consider a global complexity bound of regularized Newton methods for the unconstrained convex optimization. The global complexity bound is an upper bound of the number of iterations required to get an approximate solution x such that f(x)− inf f(y) ≤ ε, where ε is a given positive constant. Recently, Ueda and Yamashita proposed the regularized Newton method whose global complexity bound is O...

An Accelerated Block-Parallel Newton Method via Overlapped Partitioning

This paper presents an overlapped block-parallel Newton method for solving large nonlinear systems. The graph partitioning algorithms are first used to partition the Jacobian into weakly coupled overlapping blocks. Then the simplified Newton iteration is directly performed, with the diagonal blocks and the overlapping solutions assembled in a weighted average way at each iteration. In the algor...

Accelerated Inexact Newton

Schrödinger-Newton equation with complex Newton constant and induced gravity

In the reversible Schrödinger-Newton equation a complex Newton coupling G exp(−iα) is proposed in place of G. The equation becomes irreversible and all initial one-body states are expected to converge to solitonic stationary states. This feature is verified numerically. For two-body solutions we point out that an effective Newtonian interaction is induced by the imaginary mean-fields as if they...

An Accelerated Newton Method for Equations with Semismooth Jacobians and Nonlinear Complementarity Problems: Extended Version

We discuss local convergence of Newton’s method to a singular solution x∗ of the nonlinear equations F (x) = 0, for F : IR → IR. It is shown that an existing proof of Griewank, concerning linear convergence to a singular solution x∗ from a starlike domain around x∗ for F twice Lipschitz continuously differentiable and x∗ satisfying a particular regularity condition, can be adapted to the case i...