An efficient block-oriented approach to parallel sparse Cholesky factorization
SIAM Journal on Scientific Computing
Improving the ratio of memory operations to floating-point operations in loops
ACM Transactions on Programming Languages and Systems (TOPLAS)
Auto-blocking matrix-multiplication or tracking BLAS3 performance from source code
PPOPP '97 Proceedings of the sixth ACM SIGPLAN symposium on Principles and practice of parallel programming
Data traffic reduction schemes for Cholesky factorization on asynchronous multiprocessor systems
ICS '89 Proceedings of the 3rd international conference on Supercomputing
Storage reorganization techniques for matrix computation in a paging environment
Communications of the ACM
Language support for Morton-order matrices
PPoPP '01 Proceedings of the eighth ACM SIGPLAN symposium on Principles and practices of parallel programming
Automatically tuned linear algebra software
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
The Matrix Template Library: Generic Components for High-Performance Scientific Computing
Computing in Science and Engineering
Recursive Array Layouts and Fast Matrix Multiplication
IEEE Transactions on Parallel and Distributed Systems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Fast additions on masked integers
ACM SIGPLAN Notices
Is Morton layout competitive for large two-dimensional arrays yet?: Research Articles
Concurrency and Computation: Practice & Experience - 10th International Workshop on Compilers for Parallel Computers (CPC 2003)
Analyzing block locality in Morton-order and Morton-hybrid matrices
MEDEA '06 Proceedings of the 2006 workshop on MEmory performance: DEaling with Applications, systems and architectures
A paradigm for parallel matrix algorithms: scalable cholesky
Euro-Par'05 Proceedings of the 11th international Euro-Par conference on Parallel Processing
Representation-transparent matrix algorithms with scalable performance
Proceedings of the 21st annual international conference on Supercomputing
Analyzing block locality in Morton-order and Morton-hybrid matrices
ACM SIGARCH Computer Architecture News
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
Communication-avoiding parallel strassen: implementation and performance
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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A blossoming paradigm for block-recursive matrix algorithms is presented that, at once, attains excellent performance measured by• time• TLB misses• L1 misses• L2 misses• paging to disk• scaling on distributed processors, and• portability to multiple platforms.It provides a philosophy and tools that allow the programmer to deal with the memory hierarchy invisibly, from L1 and L2 to TLB, paging, and interprocessor communication. Used together, they provide a cache-oblivious style of programming.Plots are presented to support these claims on an implementation of Cholesky factorization crafted directly from the paradigm in C with a few intrinsic calls. The results in this paper focus on low-level performance, including the new Morton-hybrid representation to take advantage of hardware and compiler optimizations. In particular, this code beats Intel's Matrix Kernel Library and matches AMD's Core Math Library, losing a bit on L1 misses while winning decisively on TLB-misses.