Abstract With the recent realization of exascale performance by Oak Ridge National Laboratory’s Frontier supercomputer, reducing communication in kernels like QR factorization has become even more imperative. Low-synchronization Gram-Schmidt methods, first introduced Świrydowicz et al. ( Numer. Lin. Alg. Appl. 28(2):e2343, 2020), have been shown to improve scalability Arnoldi method high-perfor...

In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. the addressed set-up, dimension decision variable can be extremely high and objective function nonsmooth. The general algorithm consists two main steps: consensus step an update on single block variable, which is then broadcast to neighbors. Three...

In this paper, we use a combination of Legendre and Block-Pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.The nonlinear part of the integral equation is approximated by Hybrid Legen-dre Block-Pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. We give some numerical examples. To showapplicability of...