Relaxed reflection methods for feasibility and matrix completion problems

该项目建议进一步发展非线性收敛理论，并提供具体问题的实施。许多应用和纯问题都需要解一大组线性或非线性方程(或不等式)。高效、可并行化的方法基于迭代投影或反射算法，这些算法聚集了关于单个方程的信息。这一理论在线性情况下得到了很好的发展，但并没有解释它们经常非常成功的许多重要应用(例如光学像差校正、蛋白质重建、层析成像、压缩传感)。该项目还计划提供启发式方法，以帮助解释为什么算法在一类应用程序上表现良好，而在另一类应用程序上却失败。

The project proposes to further develop the non-linear convergence theory, and to provide problem-specific implementations. Many applied and pure problems require solution of a large set of linear or nonlinear equations (or inequalities). Highly effective, parallelisable methods are based on iterated projection or reflection algorithms which aggregate information about individual equations. The theory is well developed in the linear case, but does not explain many important applications for which they are often highly successful (eg optical aberration correction, protein reconstruction, tomography, compressed sensing). The project also plans to provide heuristics to help explain why an algorithm performs well on one class of applications but fails on another.