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Chebyshev solution of large linear systems

✍ Scribed by J.B. Rosen

Publisher
Elsevier Science
Year
1967
Tongue
English
Weight
636 KB
Volume
1
Category
Article
ISSN
0022-0000

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✦ Synopsis

The general problem considered is that of solving a linear system of equations which is singular or almost singular. A method is described which obtains a "solution" to the system which is stable with respect to small changes in the matrix elements. This method will solve an overdetermined system in m variables and n equations (m < n) even when the system rank is less than m, and should therefore be very useful in many statistical applications. In this case the error of the system is minimized in the Chebyshev norm using a linear programming formulation and solution. A numerical example using the Hilbert matrix is described in detail.

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✍ NIKOLAUS GEERS; ROLAND KLEES πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 575 KB

We developed a direct out-of-core solver for dense non-symmetric linear systems of 'arbitrary' size N;N. The algorithm fully employs the Basic Linear Algebra Subprograms (BLAS), and can therefore easily be adapted to different computer architectures by using the corresponding optimized routines. We