Newton’s iteration has quadratic convergence for simple roots. We present a Newton-based iteration scheme with quadratic convergence for multiple roots of systems of analytic functions. This is a report on work in progress. 1. Newton Iteration, Approximate Roots and γ-Theorems 1.1. Newton Iteration. Let f : Cn → Cn be an analytic function. Newton’s method for solving f = 0 consists in approxima...

We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward...

Effective target detection and tracking has always been a research hotspot in the field of radar, multi-target is focus radar at present. In order to effectively deal with issue outlier removal track initiation determination process tracking, this paper proposes an improved backward smoothing method based on label iterative processing. This corrects loophole original method, which can cause est...

<p style='text-indent:20px;'>We develop a backward stochastic differential equation based probabilistic machine learning method, which formulates class of neural networks as optimal control problem. An efficient gradient descent algorithm is introduced with the computed through equation. Convergence analysis for optimization and numerical experiments applications are carried out to valida...

A numerical elimination method is presented in this paper for floating-point computation in polynomial algebra. The method is designed to calculate one or more polynomials in an elimination ideal by a sequence of matrix rank/kernel computation. The method is reliable in numerical computation with verifiable stability and a sensitivity measurement. Computational experiment shows that the method ...