Functions Whose Best Rational Tchebycheff Approximations Are Polynomials

Barry W. Boehm

ResearchPublished 1964

Let r*(n,m,f) denote the best approximation to a function f by a rational function which is the quotient of a polynomial of degree n by a polynomial of degree m. The following results are typical. r*(n,m,f) is a polynomial for all n and m if and only if f is a constant. r*(n,n,f) is a polynomial for all n if and only if f is a constant plus a multiple of a Tchebycheff polynomial. For any c 1, there exist continuous nonpolynomial functions f such that, for all n, r*(cn,n,f) is a polynomial. 20 pp.

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  • Copyright: RAND Corporation
  • Availability: Available
  • Year: 1964
  • Print Format: Paperback
  • Paperback Pages: 20
  • Paperback Price: $20.00
  • Document Number: R-427/1-PR (Abridgement I)

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RAND Style Manual
Boehm, Barry W., Functions Whose Best Rational Tchebycheff Approximations Are Polynomials, RAND Corporation, R-427/1-PR (Abridgement I), 1964. As of September 24, 2024: https://www.rand.org/pubs/reports/R427z1.html
Chicago Manual of Style
Boehm, Barry W., Functions Whose Best Rational Tchebycheff Approximations Are Polynomials. Santa Monica, CA: RAND Corporation, 1964. https://www.rand.org/pubs/reports/R427z1.html. Also available in print form.
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