6533b856fe1ef96bd12b25e0
RESEARCH PRODUCT
Third-order accurate monotone cubic Hermite interpolants
Francesc AràndigaDionisio F. Yáñezsubject
Hermite polynomialsApplied MathematicsHarmonic meanDerivativeFunction (mathematics)computer.software_genreThird orderMonotone polygonComputer Aided DesignApplied mathematicsMATLABcomputercomputer.programming_languageMathematicsdescription
Abstract Monotonicity-preserving interpolants are used in several applications as engineering or computer aided design. In last years some new techniques have been developed. In particular, in Arandiga (2013) some new methods to design monotone cubic Hermite interpolants for uniform and non-uniform grids are presented and analyzed. They consist on calculating the derivative values introducing the weighted harmonic mean and a non-linear variation. With these changes, the methods obtained are third-order accurate, except in extreme situations. In this paper, a new general mean is used and a third-order interpolant for all cases is gained. We perform several experiments comparing the known techniques as the method proposed by Fritsch and Butland using the Brodlie’s function, PCHIP program of Matlab (Moler, 2004; Wolberg and Alfy, 2002) with the new algorithm.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-08-01 | Applied Mathematics Letters |