Papers › A more direct and better variant of New Q-Newton's method Backtracking for m equations...
A more direct and better variant of New Q-Newton's method Backtracking for m equations in m variables
Tuyen Trung Truong
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
In this paper we apply the ideas of New Q-Newton's method directly to a system of equations, utilising the specialties of the cost function f=||F||², where F=(f₁,…,fₘ). The first algorithm proposed here is a modification of Levenberg-Marquardt algorithm, where we prove some new results on global convergence and avoidance of saddle points. The second algorithm proposed here is a modification of New Q-Newton's method Backtracking, where we use the operator ∇²f(x)+δ||F(x)||^τ instead of ∇²f(x)+δ||∇f(x)||^τ. This new version is more suitable than New Q-Newton's method Backtracking itself, while currently has better avoidance of saddle points guarantee than Levenberg-Marquardt algorithms. Also, a general scheme for second order methods for solving systems of equations is proposed. We will also discuss a way to avoid that the limit of the constructed sequence is a solution of H(x)^⊺F(x)=0 but not of F(x)=0.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections