The Lie-Group Shooting Method for Quasi-Boundary Regularization of Backward Heat Conduction Problems Chih-Wen Chang1, Chein-Shan Liu2 and Jiang-Ren Chang1 Summary By using a quasi-boundary… (More)

The Lie-Group Shooting Method for Nonlinear Two-Point Boundary Value Problems Exhibiting Multiple Solutions Chein-Shan Liu1 Summary The present paper provides a Lie-group shooting method for the… (More)

The Newton algorithm based on the “continuation” method may be written as being governed by the equation ( ) j x t + 1 ( ) 0, ij i j B F x − = where Fi (xj) = 0, i, j = 1, ...n are nonlinear… (More)

Iterative algorithms for solving a system of nonlinear algebraic equations (NAEs): Fi(x j) = 0, i, j= 1,. . . ,n date back to the seminal work of Issac Newton. Nowadays a Newton-like algorithm is… (More)

Here we develop a general purpose pre/post conditioner T, to solve an ill-posed system of linear equations, Ax = b. The conditioner T is obtained in the course of the solution of the Laplace… (More)

Instead of the Tikhonov regularization method which with a scalar being the regularization parameter, Liu et al. [1] have proposed a novel regularization method with a vector as being the… (More)

Iterative algorithms for solving a nonlinear system of algebraic equations of the type: Fi(x j) = 0, i, j = 1, . . . ,n date back to the seminal work of Issac Newton. Nowadays a Newton-like algorithm… (More)

The Tikhonov method is a famous technique for regularizing ill-posed linear problems, wherein a regularization parameter needs to be determined. This article, based on an invariant-manifold method,… (More)

We propose novel algorithms to calculate the inverses of ill-conditioned matrices, which have broad engineering applications. The vector-form of the conjugate gradient method (CGM) is recast into a… (More)

We treat an ill-posed system of linear equations by transforming it into a linear system of stiff ordinary differential equations (SODEs), adding a differential term on the left-hand side. In order… (More)