实现通信最优的并行和顺序QR分解

通信最优的并行和顺序QR与LU分解：理论与实践

Communication-optimal parallel and sequential QR and LU factorizations: theory and practice

提出并行和顺序的QR分解算法，在通信量上达到最优（最多对数因子），并保持与Householder QR相同的稳定性。

通信最优的并行和顺序QR与LU分解

Communication-optimal parallel and sequential QR and LU factorizations

提出通信量最优（至多对数因子）且与Householder QR同样稳定的并行和顺序稠密QR分解算法，并证明现有LAPACK和ScaLAPACK算法通信量渐近更大。

Implementing a smooth exact penalty function for general constrained nonlinear optimization

We build upon Estrin et al. (2019) to develop a general constrained nonlinear optimization algorithm based on a smooth penalty function proposed by Fletcher (1970, 1973b). Although Fletcher's approach has historically been considered impractical, we show that the computational kernels required are no more expensive than those in other widely accepted methods for nonlinear optimization. The main kernel for evaluating the penalty function and its derivatives solves structured linear systems. When the matrices are available explicitly, we store a single factorization each iteration. Otherwise, we…

Implementing a smooth exact penalty function for equality-constrained nonlinear optimization

We develop a general equality-constrained nonlinear optimization algorithm based on a smooth penalty function proposed by Fletcher (1970). Although it was historically considered to be computationally prohibitive in practice, we demonstrate that the computational kernels required are no more expensive than other widely accepted methods for nonlinear optimization. The main kernel required to evaluate the penalty function and its derivatives is solving a structured linear system. We show how to solve this system efficiently by storing a single factorization each iteration when the matrices are a…

串行稀疏Cholesky分解算法中可使用的一些新技术

Some new techniques to use in serial sparse Cholesky factorization algorithms

本文提出两种串行右视超节点稀疏Cholesky分解新变体，通过超节点内列重排序减少并增大非对角块，其中RLB无需浮点工作存储且不执行组装，在使用多线程BLAS时显著快于现有方法。

面向多核架构的并行分块QR分解

Parallel Tiled QR Factorization for Multicore Architectures

提出一种基于分块和动态任务调度的并行QR分解算法，通过细粒度任务并行和松同步执行，有效隐藏顺序任务，相比LAPACK的BLAS级并行方法显著提升多核性能。