ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

1991 MS Classification: 41, 65 Oja, Peeter, Tartu University, Estonia: Adaptive by monotonicity interpolating splines For given data x_{i}, f_{i}, i = 1, …, n, and partition ξ_{o} ≤ x_{1} < ξ_{1} < x_{2} < … < ξ_{n−1} < x_{n} ≤ ξ_{n} an adaptive spline S is a linear/linear rational function or quadratic polynomial in each interval [ξ_{i−1}, ξ_{i}], i = 1, …, n, satisfies S(x_{i}) = f_{i}, i = 1, …, n, boundary conditions S(x_{0}) = α, S(x_{0}) = β or S′(x_{0}) = α, S′(x_{0}) = β and belongs to C^{1}[a, b]. It has maximal number of rational intervals to preserve locally the monotonicity of data. The uniqueness and existence of such adaptive splines are proved. Similar quadratic/linear and cubic combined adaptive splines of class C^{2} preserving local convexity or concavity are known to exist only if an additional condition concerning the data holds.