Applying the unified convergence theory to other
Research gap analysis derived from 4 mathematics papers in our local library.
The gap
The paper suggests applying the unified convergence theory to other optimization methods.
Evidence profile
Stated in the conclusions and cells future research and cells research gap sections 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
- 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.
generalstated in conclusionsevidence 5/5Keywords: 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.
generalstated in cells future researchevidence 5/5Keywords: future research focus further improving convergence order new - Expanding the region of convergence for second order methods to solve nonlinear equations via the generalized moment generating function approach (2026) · Numerical Algorithms · doi
The convergence behavior of iterative algorithms depends on the initial value. - There is a need for a systematic way to derive a generalized moment generating function approach for an arbitrary second-order method.
generalstated in cells research gapevidence 5/5Keywords: convergence behavior iterative algorithms depends initial value there - Some Unified Theory for Variance Reduced Prox-Linear Methods (2026) · SIAM Journal on Optimization · doi
The paper suggests applying the unified convergence theory to other optimization methods.
generalstated in cells future researchevidence 4/5Keywords: paper suggests applying unified convergence theory other optimization
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