S(RN)1-type coupling adducts are readily prepared by the reaction between a-sulfonylesters or a-cyanosulfones and gem-dinitro compounds in ionic liquids. The reactions progress smoothly and recovered ionic liquids can be used for several iterations, as long as they are washed with water to remove alkali metallic salts. The reaction rate is slower than the corresponding S(RN)1 reaction in DMSO, ...

We study the design of polylogarithmic depth algorithms for approximately solving packing and covering semidefinite programs (or positive SDPs for short). This is a natural SDP generalization of the well-studied positive LP problem. Although positive LPs can be solved in polylogarithmic depth while using only Õ(log n/ε) parallelizable iterations [4, 33], the best known positive SDP solvers due ...

Some iterative calculations can be carried out by parallel communicating processors, and yield the same results whether or not the processors are synchronized. We show that this is the case if and only if the iteration is a contraction that is strict on orbits, with respect to an ultrametric defined on the state space. The maximum number of independent processors is given by the dimension of th...

We consider inverse iteration-based eigensolvers, which require at each step solving an “inner” linear system. We assume that this linear system is solved by some (preconditioned) Krylov subspace method. In this framework, several approaches are possible, which differ by the linear system to be solved and/or the way the preconditioner is used. This includes methods such as inexact shift-and-inv...

We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of Rn and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in terms of numerical cost and global behavior with three other methods that display the same property of cubic convergence. Moreover, we consider heuristics that greatly improve the global be...

This paper deals with the iterative solution of non-linear equations f(x) = 0. We consider integral information on f which is given by f(x Q),f•(x Q),...,f ( s ) ( X q) and J°f(t)dt. We define an intery polatory-integral method which uses integral information and which has maximal order of convergence equal to s+3. Since the maximal order of iterations which use f ( x Q ) , . . . , f ( s } ( x ...

Split Bregman methods introduced in [T. Goldstein and S. Osher, SIAM J. Imaging Sci., 2(2009), pp. 323–343] have been demonstrated to be efficient tools for solving total variation norm minimization problems, which arise from partial differential equation based image restoration such as image denoising and magnetic resonance imaging reconstruction from sparse samples. In this paper, we prove th...