Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Scientific Computing: An Introductory Survey
Scientific Computing: An Introductory Survey
Numerical Methods for Engineers with Personal Computer Applications
Numerical Methods for Engineers with Personal Computer Applications
Parallel Scientific Computing in C++ and MPI
Parallel Scientific Computing in C++ and MPI
LU-GPU: Efficient Algorithms for Solving Dense Linear Systems on Graphics Hardware
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
Cramer's rule on 2-by-2 systems
ACM SIGNUM Newsletter
Cramer's rule reconsidered or equilibration desirable
ACM SIGNUM Newsletter
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State-of-the-art software packages for solving large-scale linear systems are predominantly founded on Gaussian elimination techniques (e.g. LU-decomposition). This paper presents an efficient framework for solving large-scale linear systems by means of a novel utilization of Cramer@?s rule. While the latter is often perceived to be impractical when considered for large systems, it is shown that the algorithm proposed retains an O(N^3) complexity with pragmatic forward and backward stability properties. Empirical results are provided to substantiate the stated accuracy and computational complexity claims.