多核架构下矩阵计算的瓦片算法
Tiled Algorithms for Matrix Computations on Multicore Architectures
AI总结：
针对多核架构，研究瓦片算法以替代传统稠密数值线性代数库，实现Cholesky、LU和QR分解的高效可扩展计算。
摘要：
当前计算机架构已转向多核/众核结构。然而，当前顺序稠密数值线性代数库（如LAPACK）中的算法在多核/众核架构上并行化效果不佳。最近引入了一类新算法——瓦片算法，以规避此问题。先前研究表明，可以编写高效且可扩展的瓦片算法来执行Cholesky分解、（伪）LU分解和QR分解。本论文的目标是在多核/众核环境下研究瓦片算法，并提供利用当前架构提升性能的新算法，同时保持现有库的稳定性和鲁棒性。
英文摘要：
The current computer architecture has moved towards the multi/many-core structure. However, the algorithms in the current sequential dense numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multi/many-core architectures. A new family of algorithms, the tile algorithms, has recently been introduced to circumvent this problem. Previous research has shown that it is possible to write efficient and scalable tile algorithms for performing a Cholesky factorization, a (pseudo) LU factorization, and a QR factorization. The goal of this thesis is to study tiled algorithms in a multi/many-core setting and to provide new algorithms which exploit the current architecture to improve performance relative to current state-of-the-art libraries while maintaining the stability and robustness of these libraries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
