Affiliation:
1. Massachusetts Institute of Technology
Abstract
If numerical analysts understand anything, surely it must be Gaussian elimination. This is the oldest and truest of numerical algorithms. To be precise, I am speaking of Gaussian elimination with partial pivoting, the universal method for solving a dense, unstructured
n X n
linear system of equations
Ax = b
on a serial computer. This algorithm has been so successful that to many of us, Gaussian elimination and
Ax = b
are more or less synonymous. The chapter headings in the book by Golub and Van Loan [3] are typical -- along with "Orthogonalization and Least Squares Methods," "The Symetric Eigenvalue Problem," and the rest, one finds "Gaussian Elimination," not "Linear Systems of Equations."
Publisher
Association for Computing Machinery (ACM)
Reference9 articles.
1. On the Asymptotic Complexity of Matrix Multiplication
2. G. H. Golub and C. F. Van Loan Matrix Computations Johns Hopkins University Press Baltimore Maryland 1983. G. H. Golub and C. F. Van Loan Matrix Computations Johns Hopkins University Press Baltimore Maryland 1983.
3. How Can We Speed Up Matrix Multiplication?
4. On the average number of steps of the simplex method of linear programming
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