on {0, 1/10,. . . , 9/10, 1} to the functionf (x) = x -k exp (x) + exp (2x)/100. This is a minimization problem with four parameters, a~, a2, as, a4. When MINI was run initially with arguments STPâ€¦ (More)

This paper casts doubt on the feasibility of perfect subroutines or perfect hardware for mathematical functions, in particular by conversion from double precision. It suggests a slightly relaxedâ€¦ (More)

Consider the solution of systems of two linear equations, for which Cramer's rule has some attractions [3]. It is claimed by Moler [3] that Cramer's rule is of unsatisfactory accuracy even in thisâ€¦ (More)

In polynomial Chebyshev approximat ion on an interval by the Remez algorithm, one can use a power basis or a Chebyshev polynomial basis for polynomials. More generally, in rat ional Chebyshevâ€¦ (More)

Maehly 's second m e t h o d is an algori thm for finding lhe best Chebyshev approximation to a cont inuous func t ion (m a finite interval. This note describes a small simplification of the computatâ€¦ (More)

is in general impossible to meet. For example, arguments to the square root function from the interval [1,4] should be mapped into [1,2]; but there are twice as many floating point numbers in [1,4]â€¦ (More)

A sufficient condition is given for best Chebyshev approximations of the form a+bÏ•(cx) to be characterized by alternation of their error curve. Several examples are given of Ï• for which alternationâ€¦ (More)

A Remez algorithm with simultaneous exchanges is described for minimax approximation with Lagrange-type interpolation by varisolvent families, in particular, families of Meinardus and Schwedt. Esâ€¦ (More)

Chebyshev approximation on an interval and closed subsets by a Haar subspace are considered. The closeness of best approximations on subsets to the best approximation on the interval is examined. Itâ€¦ (More)