An improved gradient and Newton algorithm for fast rolling problem.

Finite element method (FEM) is an efficient computational algorithm and has been widely applied to strip rolling process. For on-line application, two key issues, i.e. calculating speed and calculating precious, have to be achieved to the industrial requirements. In this paper, we present an algorithm named improved gradient and Newton method that combines Cholesky factorization method and Newton method to solve the strip rolling problem. In the proposed algorithm, Cholesky factorization method is used to search descend direction (gradient), while Newton method mainly focuses on searching step factor. Due to the excellent ability of Cholesky factorization method in solving the decomposed equations of FEM, the calculating speed is absolutely improved. Accordingly, the ability of Newton method in finding exact step factor improves the calculating precious. The global convergence of proposed algorithm can be proved according to the convergence proof of Newton method. Computational experiments demonstrate that the proposed algorithm is efficient and steady in strip rolling. [ABSTRACT FROM AUTHOR]