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A Modified Newton Method For Solving Non-Linear Algebraic Equations, Satya N. Atluri, Chein-Shan Liu, Chung-Lun Kuo

Journal of Marine Science and Technology

The Newton algorithm based on the “continuation” method may be written as being governed by the equation xj(t) + Bij-1 Fi(xj) = 0, where Fi(xj) = 0, i, j = 1, …n are nonlinear algebraic equations (NAEs) to be solved, and Bij = ∂Fi /∂xj is the corresponding Jacobian matrix. It is known that the Newton's algorithm is quadratically convergent; however, it has some drawbacks, such as being sensitive to the initial guess of solution, and being expensive in the computation of the inverse of Bij at each iterative step. How to preserve the convergence speed, and to remove the …