The need for a method that can improve the convergence of iterative numerical techniques
Research gap analysis derived from 4 mathematics papers in our local library.
The gap
The need for a method that can improve the convergence of iterative numerical techniques. The limitation of the Newton process for determining the root of an equation.
Evidence profile
Sourced from the conclusions and future-work section and stated research gap of the source papers, classified as general, drawn from work published between 1962 and 2026, spanning 4 journals. Those papers have been cited 4 times in total.
Research trend
Established — well-defined area with open sub-problems.
Supporting evidence — 4 representative gaps
- Stochastic Gradient Descent for Incomplete Tensor Linear Systems (2026) · BIT Numerical Mathematics · doi
Alternatively, the convergence of iterative methods other than SGD, such as Gauss-Seidel variants, could be studied using a proof technique similar to that of Theorem 2.
generalconclusionsKeywords: alternatively convergence iterative gauss seidel variants studied using proof technique similar theorem - Increasing the order of convergence in Jacobian-free iterative schemes: applications to real-life problems (2026) · Numerical Algorithms · doi
Future research can focus on further improving the convergence order of the new methods. The authors suggest exploring the application of the new methods to other types of problems. Further research can investigate the use of auxiliary functions and weighting operators in other iterative schemes.
generalfuture-work sectionevidence 5/5Keywords: future research focus further improving convergence order new - A note on the fitting of certain types of experimental data* (1962) · Statistica Neerlandica · cited 4× · doi
The need for a method that can improve the convergence of iterative numerical techniques. The limitation of the Newton process for determining the root of an equation.
generalstated research gapevidence 5/5Keywords: need method improve convergence iterative numerical techniques limitation - Methods for solving variational inequalities with Markovian stochasticity (2026) · Optimization methods & software · doi
To extend the proposed method to other optimization problems. To investigate the effect of different parameters on the convergence of the algorithm. To compare the proposed method with other methods in various scenarios.
generalfuture-work sectionevidence 5/5Keywords: extend proposed method other optimization problems investigate effect
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