Dealing with multiple roots of nonlinear equations
Research gap analysis derived from 3 mathematics papers in our local library.
The gap
Dealing with multiple roots of nonlinear equations. Developing methods that can handle unknown multiplicity. Achieving robust convergence properties.
Evidence profile
Sourced from the stated research gap and stated challenges of the source papers, classified as general, spanning 3 journals.
Research trend
Established — well-defined area with open sub-problems.
Supporting evidence — 4 representative gaps
- A New Three-Step Modification of a Fifth-Order Iterative Method with Weight Functions for Solving Nonlinear Equations (2026) · World Scientific News · doi
Existing methods have limitations in terms of convergence order and computational cost. There is a need for more efficient and competitive methods for solving nonlinear equations.
generalstated research gapevidence 5/5Keywords: existing methods have limitations terms convergence order computational - Simultaneous determination of multiple zeros via Schröder–Ehrlich-type corrections (2026) · Numerical Algorithms · doi
Standard iterative methods often exhibit a significant loss of order of convergence when applied to problems involving multiple roots. There is a need for numerical procedures specifically designed for the simultaneous approximation of multiple roots of nonlinear equations.
generalstated research gapevidence 5/5Keywords: standard iterative methods often exhibit significant loss order - Computational Mathematics and Numerical Techniques (2026) · Zenodo (CERN European Organization for Nuclear Research) · doi
The paper identifies the need for efficient and reliable methods for computing the roots of non-linear scalar equations. The paper notes that existing methods may have limitations, such as slow convergence or requiring the computation of derivatives.
generalstated research gapevidence 5/5Keywords: paper identifies need efficient reliable methods computing roots - Simultaneous determination of multiple zeros via Schröder–Ehrlich-type corrections (2026) · Numerical Algorithms · doi
Dealing with multiple roots of nonlinear equations. Developing methods that can handle unknown multiplicity. Achieving robust convergence properties.
generalstated challengesevidence 4/5Keywords: dealing multiple roots nonlinear equations developing methods handle
Questions about this gap
Explore this gap further
Run this gap as a query across open scholarly engines for the latest related literature.
Working on this gap? Review it with us.
Science AI Journal reviews manuscripts in one pass with 8 specialised AI agents calibrated on 69,000+ real peer reviews.
Tools for your next paper
Related gaps in Mathematics
- The lack of unification of underlying physical lawsThe lack of unification of underlying physical laws in current AI safety research. The separation of legal systems from the physical world.
- To apply the suggested method to other nonlinear partialTo apply the suggested method to other nonlinear partial differential equations. To improve the method for time-dependent boundary condition…
- The paper identifies a gap in prior work regardingThe paper identifies a gap in prior work regarding the properties of intermediate and modal propositional logics. It aims to fill this gap b…
- Discuss the computational cost of the preconditioningDiscuss the computational cost of the preconditioning transformation. The numerical example is limited to a specific problem.