Scalable parallelization of FLAME code via the workqueuing model
ACM Transactions on Mathematical Software (TOMS)
SuperMatrix: a multithreaded runtime scheduling system for algorithms-by-blocks
Proceedings of the 13th ACM SIGPLAN Symposium on Principles and practice of parallel programming
Families of algorithms related to the inversion of a Symmetric Positive Definite matrix
ACM Transactions on Mathematical Software (TOMS)
Solving dense linear systems on platforms with multiple hardware accelerators
Proceedings of the 14th ACM SIGPLAN symposium on Principles and practice of parallel programming
Automating the generation of composed linear algebra kernels
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
Goal-Oriented and Modular Stability Analysis
SIAM Journal on Matrix Analysis and Applications
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We consider the problem of developing formally correct dense linear algebra libraries. The problem would be solved convincingly if, starting from the mathematical specification of a target operation, it were possible to generate, implement and analyze a family of correct algorithms that compute the operation. This thesis presents evidence that for a class of dense linear operations, systematic and mechanical development of algorithms is within reach. It describes and demonstrates an approach for deriving and implementing, systematically and even mechanically, proven correct algorithms. It also introduces a systematic procedure to analyze, in a modular fashion, numerical properties of the generated algorithms.