Rational Cubic Spline For Shape Preserving Interpolation
| dc.contributor.author | Abdul Karim, Samsul Ariffin | |
| dc.date.accessioned | 2018-01-23T01:51:31Z | |
| dc.date.available | 2018-01-23T01:51:31Z | |
| dc.date.issued | 2017-08 | |
| dc.description.abstract | A new rational cubic spline function of the form cubic numerator and quadratic denominator has been proposed. This rational cubic spline has three parameters. The parameters can be used to modify the shape of the interpolating curve. Shape preservation for positivity, monotonicity and convexity interpolations as well as constrained data interpolation which the data lie on one side of a given constraint line are investigated in details. The shape preservation conditions are derived on one parameter while the other two parameters provide freedom in controlling the final interpolating curves. Degree smoothness attained is C1 . Local control of the rational interpolant for value-control, inflection point and convexity control also is considered. The proposed rational cubic splines has able to reduce the complexity of the non-linear equations. Besides, the error analysis of the rational interpolant when the interpolated function is C3 also has been discussed. The univariate rational cubic spline is extended to the bivariate cases using partially blended rational bi-cubic function. The proposed partially blended rational bi-cubic surface have 12 parameters and 8 of them are free to be utilized to control the shape of the resulting surface. The conditions for shape preservation of positive, monotonic, convex interpolations and constrained interpolation for data that lying on one side of the constraint surface are derived on four parameters. Numerical examples are illustrated graphically to show the capability of the proposed schemes. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/5444 | |
| dc.language.iso | en | en_US |
| dc.publisher | Universiti Sains Malaysia | en_US |
| dc.subject | Rational cubic spline | en_US |
| dc.subject | for shape Preserving interpolation | en_US |
| dc.title | Rational Cubic Spline For Shape Preserving Interpolation | en_US |
| dc.type | Thesis | en_US |
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