On minimax solutions of linear equations | Zendy

R. P. Tewarson | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

On minimax solutions of linear equations

Author(s) -

R. P. Tewarson

Publication year - 1972

Publication title -

the computer journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.319

H-Index - 64

eISSN - 1460-2067

pISSN - 0010-4620

DOI - 10.1093/comjnl/15.3.277

Subject(s) - simplex algorithm , minimax , linear programming , chebyshev iteration , system of linear equations , revised simplex method , chebyshev filter , mathematics , linear equation , linear system , simplex , chebyshev nodes , minimax approximation algorithm , chebyshev polynomials , mathematical optimization , computer science , mathematical analysis , combinatorics

where E" is the n dimensional Euclidean space and r,(jc) denotes the ith element of r{x). An excellent discussion of the above problem and several algorithms for its solution are given by Cheney (1966). He calls one of these algorithms, which is due to Stiefel (1959, 1960, 1963), the ascent algorithm. In this paper, we shall reformulate the ascent algorithm (Cheney, 1966, p. 45) by making use of the Generalised inverse (Penrose, 1955, 1956). This will make it possible for us to express the algorithm in the tableau form associated with the Revised Simplex Method for the solution of linear programming problem (Kiinzi, Tzschach, and Zehnder, 1968). The principal advantages of the algorithm given in this paper are:

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research