This paper proposes a randomized iterative method called Sequential Preconditioned Conjugate Gradient Method (SPCG) for large-scale linear statistical models, which significantly reduces computational…

This paper constructs strictly convex quadratic problems and initial points for which the long Barzilai--Borwein method does not converge root-superlinearly.

The paper analyzes a new class of asynchronous adaptive first-order optimization methods and proves their stochastic convergence rate is O(1/sqrt{t}) for non-convex functions.

This paper investigates the convergence and stability of equilibria in bimatrix two-player games using the optimistic exponential weights method, allowing step sizes to differ.

This paper proposes a data collection strategy using solver iterates to augment datasets for training generative models, improving the efficiency of the data-model-optimization loop in one-sided box-c…

The paper proposes FOAM, an adaptive damping method that stabilizes the Shampoo optimization algorithm by dynamically controlling damping and eigendecomposition frequency, thereby reducing staleness-i…

The paper introduces Iteris, an agentic research system, demonstrating its capability to generate numerical evidence, constructions, and proof drafts for open problems in computational mathematics, re…

This paper analyzes the computational complexity of evaluating recurrent functions, showing that the complexity depends heavily on how the input offsets are encoded and the structure of the recurrence…

This paper introduces Stale Synchronous Parallel mode of execution for parallel sparse triangular linear system solve and presents a scheduler that achieves geometric-mean speed-ups of 7-30% over Grow…

The authors introduce a quantum empirical operator and use it to prove a universal achievability result for composite quantum hypothesis testing.

This paper proposes a Hybrid Augmented Lagrangian (HyAL) method that integrates the constraint-handling strengths of the AL framework with the exploratory power of population-based search.

Introduce Deep Second-Order Stochastic Residual Method (D2SRM) for high-dimensional, Hessian-dependent fully nonlinear parabolic PDEs, establish well-posedness, and develop population-level convergenc…

The paper introduces an operator calculus for population-based optimization methods, establishing a modular Lyapunov principle for their convergence analysis.

This paper proposes a unified sparse background-grid framework for the Material Point Method (MPM), significantly reducing computational time and memory usage in large-scale simulations where the mate…

This paper derives multivariate generating functions to refine the enumeration of Fibonacci polyominoes.

This paper develops a convergence theory and runtime bound for closed-loop generative selection in computational drug discovery, showing that elitism makes the search absorbing and proving almost-sure…