Error analysis of the derivative of rational interpolation with a linear denominator

References

• Schultz , M. H. 1973 . Spline Analysis , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• de Boor , C. 1978 . A Practical Guide to Splines , New York : Springer-Verlag .
   Google Scholar
• Chui , C. K. 1988 . Multivariate Splines (SIAM)
   Google Scholar
• Passow , E. and Poulier , J. A. 1977 . Monotone and convex spline interpolation . SIAM Journal of Numerical Analysis , 14 : 904 – 909 .
   Web of Science ®Google Scholar
• McAllister , D. F. and Poulier , J. A. 1981 . An algorithm for computing a shape preserving osculatory quadratic spline . ACM Transactions on Mathematical Software , 7 : 331 – 347 .
   Web of Science ®Google Scholar
• Fritsch , F. N. and Butland , J. 1984 . A method for constructing local monotone piecewise cubic interpolation . SIAM Journal on Scientific and Statistical Computing , 5 : 303 – 304 .
   Google Scholar
• Gregory , J. A. 1986 . Shape preserving spline interpolation . Computer-Aided Design , 18 : 53 – 57 .
   Web of Science ®Google Scholar
• DeVore , A. and Yan , Z. 1986 . Error analysis for piecewise quadratic curve fitting algorithms . Computer Aided Geometric Design , 3 : 205 – 215 .
   Google Scholar
• Goodman , T. N.T. and Unsworth , K. 1988 . Shape preserving interpolation by curvature continuous parametric curves . Computer Aided Geometric Design , 5 : 323 – 340 .
   Google Scholar
• Brodlie , K. W. and Butt , S. 1991 . Preserving convexity using piecewise cubic interpolation . Computers and Graphics , 15 : 15 – 23 .
   Web of Science ®Google Scholar
• Greiner , K. 1991 . A survey on univariate data interpolation and approximation by splines of given shape . Mathematical Computation and Modelling , 15 : 97 – 106 .
   Google Scholar
• Piegl , L. 1991 . On NURBS: a survey . IEEE Computer Graphics and Application , 11 : 55 – 71 .
   Web of Science ®Google Scholar
• Gregory , J. A. and Delbourgo , R. 1982 . Piecewise rational quadratic interpolation to monotonic data . IMA Journal of Numerical Analysis , 2 : 123 – 130 .
   Web of Science ®Google Scholar
• Lahtinen , A. 1992 . On the choice of parameters in shape-preserving quadratic spline interpolation . Journal of Computational and Applied Mathematics , 39 : 109 – 113 .
   Google Scholar
• Schmidt , J. W. and Hess , W. 1987 . Positive interpolation with rational quadratic spline . Computing , 38 : 261 – 267 .
   Web of Science ®Google Scholar
• Sarfraz , M. 1992 . Convexity preserving piecewise rational interpolation for planar curves . Bulletin of the Korean Mathematical Society , 29 : 193 – 200 .
   Google Scholar
• Gregory , J. A. , Sarfraz , M. and Yuen , P. K. 1994 . Interactive curve design using C 2 rational splines . Computers and Graphics , 18 : 153 – 159 .
   Web of Science ®Google Scholar
• Sarfraz , M. 1994 . Generalized geometric interpolation for rational cubic splines . Computers and Graphics , 18 : 61 – 72 .
   Google Scholar
• Duan , Q. , Djidjeli , K. , Price , W. G. and Twizell , E. H. 1998 . Rational cubic spline based on function values . Computers and Graphics , 22 : 479 – 486 .
   Web of Science ®Google Scholar
• Duan , Q. , Djidjeli , K. , Price , W. G. and Twizell , E. H. 1999 . The approximation properties of some rational cubic splines . International Journal of Computer Mathematics , 72 : 155 – 166 .
   Web of Science ®Google Scholar
• Duan , Q. , Djidjeli , K. , Price , W. G. and Twizell , E. H. 2000 . Weighted rational cubic spline interpolation and its approximation . Journal of Computational and Applied Mathematics , 117 : 121 – 135 .
   Web of Science ®Google Scholar
• Duan , Q. , Liu , A. and Cheng , F. 2001 . Constrained rational cubic spline and its application . Journal of Computational Mathematics , 19 : 143 – 150 .
   Google Scholar
• Duan , Q. , Wang , L. and Twizell , E. H. 2003 . A novel approach to the convexity control of interpolant curves . Communications in Numerical Methods in Engineering , 19 : 833 – 845 .
   Web of Science ®Google Scholar
• Zhang , J. K. and Duan , Q. 1986 . The derivative expression and derivative value estimation of cubic Hermite interpolation . Journal of Shandong University , 21 : 7 – 15 .
   Google Scholar