Alternatively, the convergence of iterative methods other than SGD, such as Gauss-Seidel variants, could be studied
Research gap analysis derived from 4 mathematics papers in our local library.
The gap
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.
Evidence profile
Sourced from the stated research gap and conclusions and future work of the source papers, classified as general, spanning 4 journals.
Research trend
Established — well-defined area with open sub-problems.
Supporting evidence — 4 representative gaps
- Random Nonlinear Fusion Frames from Averaged Operator Iterations (2026) · Results in Mathematics · doi
Convergence guarantees for randomized iterative methods are often stated in expectation, while almost sure quantitative convergence rates remain more difficult to establish. There is a need for a general convergence theory for random iterations of averaged operators on Hilbert spaces. The existing literature lacks a unifying framework that includes various iterative methods in analysis, signal processing, and optimization.
generalstated research gapKeywords: convergence guarantees randomized iterative methods often stated expectation - On convergence rates of stochastic gradient descent for linear inverse problems (2026) · Numerische Mathematik · doi
Theoretical justification of stochastic gradient methods in the context of ill-posed problems remains underdeveloped. Existing results typically yield only suboptimal rates. There is a need to establish order-optimal convergence rates for stochastic gradient methods applied to linear ill-posed problems in Hilbert spaces.
generalstated research gapevidence 5/5Keywords: theoretical justification stochastic gradient methods context ill-posed problems - 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.
generalconclusionsevidence 5/5Keywords: alternatively convergence iterative gauss seidel variants studied using proof technique similar theorem - Matrix-Free Stochastic Calculation of Operator Norms Without Using Adjoints (2026) · SIAM Journal on Matrix Analysis and Applications · doi
Algorithm 1 is a stochastic method for computing the operator norm of a linear map A between real Hilbert spaces and it only uses applications of the operator and computations of norms and inner products of vectors. We show almost sure convergence of the value to the operator norm.
generalfuture workevidence 4/5Keywords: operator norm algorithm stochastic computing linear real hilbert spaces uses applications computations norms inner products
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