Chebyshev Solution of n+1 Linear Equations in n + 1nUnknowns

ABSTRACT

An algorithm is presented for finding a solution, and the value of a solution, to n + 1 linear equations in n unknowns. The arrangement of the computation makes it convenient for use in computing Chebyshev-type approximations by polynomials. The algorithm is particularly efficient if only the value of a solution is desired.

REFERENCES

• 1: M0URSUND, D. G. Applications of hill climbing techmques to computing Ahebyshev approximations. In preparation.
• 2: VALLE POUSSIN, C. J., DE LA. Sur la mthode de lapproximation minimum. Ann. Soc. Sci. Bruxelles, Seconde Partie, Memoires 35, pp. 1-16 Bruxelles, 1911.
• 3: RBMEZ, E. YA. General computational methods of Chebyshev approximation. In Prob Iems with linear real parameters. Izd. Akad., Nauk Ukrair. SSP. Kiev, 1957 (Russian). (A mimeographed translation is available in two volumes from the Office of Technical Services, Dept. of Commerce, Washington 25, D. C.)
• 4: STIEFEL, E. Note on Jordon elimination, linear programming and Tchebyshev approxi mation. Numer. Math. 2 (1960), 1-17.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Linear systems (direct and iterative methods)

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.2 Approximation
          Subjects: Chebyshev approximation and theory

General Terms:
Performance, Theory