The algebraic eigenvalue problem
The algebraic eigenvalue problem
Average-case stability of Gaussian elimination
SIAM Journal on Matrix Analysis and Applications
Proceedings of the fourth workshop on I/O in parallel and distributed systems: part of the federated computing research conference
Locality of Reference in LU Decomposition with Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
GEMM-based level 3 BLAS: high-performance model implementations and performance evaluation benchmark
ACM Transactions on Mathematical Software (TOMS)
A survey of out-of-core algorithms in numerical linear algebra
External memory algorithms
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
A Family of High-Performance Matrix Multiplication Algorithms
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
PARA '98 Proceedings of the 4th International Workshop on Applied Parallel Computing, Large Scale Scientific and Industrial Problems
The science of deriving dense linear algebra algorithms
ACM Transactions on Mathematical Software (TOMS)
Parallel out-of-core computation and updating of the QR factorization
ACM Transactions on Mathematical Software (TOMS)
Analysis of Pairwise Pivoting in Gaussian Elimination
IEEE Transactions on Computers
Anatomy of high-performance matrix multiplication
ACM Transactions on Mathematical Software (TOMS)
Rapid development of high-performance out-of-core solvers
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Programming matrix algorithms-by-blocks for thread-level parallelism
ACM Transactions on Mathematical Software (TOMS)
Managing the complexity of lookahead for LU factorization with pivoting
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Using desktop computers to solve large-scale dense linear algebra problems
The Journal of Supercomputing
High-performance up-and-downdating via householder-like transformations
ACM Transactions on Mathematical Software (TOMS)
Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis
DAGuE: A generic distributed DAG engine for High Performance Computing
Parallel Computing
Concurrency and Computation: Practice & Experience
ACM Transactions on Mathematical Software (TOMS)
CALU: A Communication Optimal LU Factorization Algorithm
SIAM Journal on Matrix Analysis and Applications
DVFS-control techniques for dense linear algebra operations on multi-core processors
Computer Science - Research and Development
Scalable matrix decompositions with multiple cores on FPGAs
Microprocessors & Microsystems
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We show how to compute an LU factorization of a matrix when the factors of a leading principle submatrix are already known. The approach incorporates pivoting akin to partial pivoting, a strategy we call incremental pivoting. An implementation using the Formal Linear Algebra Methods Environment (FLAME) application programming interface (API) is described. Experimental results demonstrate practical numerical stability and high performance on an Intel Itanium2 processor-based server.