Power consumption and energy efficiency have become a major bottleneck in the design of new systems for high performance computing. The path to exa-scale computing requires new strategies that decrease the energy consumption of modern many-core architectures without sacrificing scalability or performance. The development of these strategies demands the use of scalable models for energy consumpt...

Necessary and sufficent conditions are obtained for ¿(/-factorization of operators on /,. In particular it is shown that uniform invertibility of the compressions of the operator is not sufficient to insure an LU-factorization of the operator, thus answering a question of de Boor, Jia, and Pinkus. The question of when a bounded linear operator on lp, 1 < p <, oo, has an Li/-factorization has be...

This paper presents a comparative study of two data mapping schemes for parallel sparse LU factorization with partial pivoting on distributed memory machines Our previous work has developed an approach that incorporates static symbolic factoriza tion nonsymmetric L U supernode partitioning and graph scheduling for this problem with D column block mapping The D mapping is commonly considered mor...

The Singular Value Decomposition (SVD) is a longstanding standard for data approximation because it is optimal in the 2 and Frobenius norms. The SVD, nevertheless, suffers from many setbacks, including computational cost, loss of sparsity in the decomposition, and the inability to be updated easily when new information arrives. Additionally, the SVD provides limited information on data features...

Quadrant Interlocking Factorization (QIF), an alternative to LU factorization, is suitable for factorizing invertible matrix A such that det(A) , 0. The QIF, with its application in parallel computing, the most efficient factorization technique yet underutilized. two forms of QIF among others, which are not only similar algorithm but also computation, WZ and WH differs applications properties. ...

In this paper, we present SILCA-Newton-Krylov, a new method for accurate, efficient and robust timedomain VLSI circuit simulation. Similar to SPICE, SILCA-Newton-Krylov uses time-difference and Newton-Raphson for solving nonlinear differential equations from circuit simulation. But different from SPICE, SILCA-Newton-Krylov explores a preconditioned flexible generalized minimal residual (FGMRES)...

We identify a class of random, dense, $n\times n$ matrices for which LU factorization with any form pivoting produces growth factor typically size at least $n/(4 \log n)$ large $n$. The condition number the can be arbitrarily chosen, and also happens transpose. Previously, no all these properties were known. generated by MATLAB function gallery('randsvd',...), they are formed as product two ran...