期刊： FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, ; ()
We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of semialgebraic sets given by Boole......
期刊： FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2020; 20 (1)
We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of closed semialgebraic sets given by Boolean......
期刊： FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2019; 19 (6)
In this paper, we investigate the sample size requirement for exact recovery of a high-order tensor of low rank from a subset of its entries. We show ......
期刊： FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2018; 18 (5)
In this paper, we study the Kurdyka-Aojasiewicz (KL) exponent, an important quantity for analyzing the convergence rate of first-order methods. Specif......
期刊： FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2018; 18 (5)
For a large class of fully nonlinear parabolic equations, which include gradient flows for energy functionals that depend on the solution gradient, th......
期刊： FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2018; 18 (4)
We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of real projective varieties. Here n......
期刊： FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2017; 17 (1)
Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a......
期刊： FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2017; 17 (1)
Historically, much of the theory and practice in nonlinear optimization has revolved around the quadratic models. Though quadratic functions are nonli......
期刊： FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2017; 17 (1)
In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating ......
期刊： FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2017; 17 (5)
This work gives a mathematical foundation for bifurcation from a stable equilibrium in the genome. We construct idealized dynamics associated with the......
