Monotone piecewise bicubic interpolation

Journal Article · Mon Apr 01 04:00:00 EST 1985 · SIAM J. Numer. Anal.; (United States)

DOI:https://doi.org/10.1137/0722023· OSTI ID:6682208

Carlson, R E; Fritsch, F N

In a 1980 paper the authors developed a univariate piecewise cubic interpolation algorithm which produces a monotone interpolant to monotone data. This paper is an extension of those results to monotone script C/sup 1/ piecewise bicubic interpolation to data on a rectangular mesh. Such an interpolant is determined by the first partial derivatives and first mixed partial (twist) at the mesh points. Necessary and sufficient conditions on these derivatives are derived such that the resulting bicubic polynomial is monotone on a single rectangular element. These conditions are then simplified to a set of sufficient conditions for monotonicity. The latter are translated to a system of linear inequalities, which form the basis for a monotone piecewise bicubic interpolation algorithm. 4 references, 6 figures, 2 tables.

• Research Organization: Lawrence Livermore National Lab., CA
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6682208
• Journal Information: SIAM J. Numer. Anal.; (United States), Journal Name: SIAM J. Numer. Anal.; (United States) Vol. 22:2; ISSN SJNAA
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
ALUMINIUM
BESSEL FUNCTIONS
DIFFERENTIAL EQUATIONS
ELEMENTS
EQUATIONS
EQUATIONS OF STATE
FUNCTIONS
HERMITE POLYNOMIALS
INTERPOLATION
ITERATIVE METHODS
MATHEMATICAL LOGIC
METALS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
POLYNOMIALS