Wellesley, Massachusetts, А К Peters, Ltd., 1995. - 404 p. - ISBN
1-56881-016-4.
Library of Congress Cataloging-in-Publication Data.
Our intention is to provide an elementary and directly applicable introduction to the computation of those (as simple as possible) spline functions, which are determined by the requirement of smooth and shape-preserving interpolation and (in two cases) the smoothing of measured or collected data.
Contents:
Preface.
Polynomial Interpolation.
The Lagrange Form of the Interpolating Polynomial.
The Newton Form of the Interpolating Polynomial.
Polygonal Paths as Linear Spline Interpolants.
General Spline Interpolants.
arious Representations of a Polygonal Path.
Evaluation by Searching an Ordered List.
Properties of Polygonal Paths.
When the Knots and Interpolation Nodes Are Different.
Parametric Polygonal Paths.
Smoothing with Polygonal Paths I.
Smoothing with Polygonal Paths II.
Quadratic Spline Interpolants.
Knots the Same as Nodes.
Optimal Initial Slope.
Periodic Quadratic Spline Interpolants with Knots the Same as Nodes.
Knots at the Midpoints of the Nodes.
Knots Variable between the Nodes.
Periodic Quadratic Spline Interpolants with Variable Knots between the Nodes.
Nodes Variable between Knots.
Quadratic Histosplines.
Quadratic Hermite Spline Interpolants.
Approximation of First Derivative Values I.
Shape Preservation through the Choice of Additional Knots.
Quadratic Splines with Given Slopes at Intermediate Points.
Cubic Spline Interpolants.
First Derivatives as Unknowns.
Second Derivatives as Unknowns.
Periodic Cubic Spline Interpolants.
Properties of Cubic Spline Interpolants.
First Derivatives Prescribed.
Second Derivatives Prescribed.
Smoothing with Cubic Spline Functions.
Smoothing with Periodic Cubic Spline Functions.
Cubic X-Spline Interpolants.
Discrete Cubic Spline Interpolants.
Local Cubic Hermite Spline Interpolants.
Approximation of Values for the First Derivative II.
Polynomial Spline Interpolants of Degree Five and Higher.
Spline Interpolants of Degree Five.
Quintic Hermite Spline Interpolants where First Derivative Values Are Specified.
Periodic Quintic Hermite Spline Interpolants.
Quintic Hermite Spline Interpolants where Second Derivatives also Are Specified.
Quartic Histosplines.
Higher-Degree Spline Interpolants.
Rational Spline Interpolants.
Rational Splines with One Freely Varying Pole.
Adaptive Rational Spline Interpolants.
Rational Spline Interpolants with a Prescribable Pole.
Rational Spline Interpolants with Two Prescribable Real Poles.
Periodic Rational Spline Interpolants with Two Prescribable Real Poles.
Rational Spline Interpolants with Two Prescribable Real or Complex Poles.
Shape Preservation of Monotone Data.
Shape Preservation of Convex or Concave Data.
Rational Histosplines.
Exponential Spline Interpolants.
First Derivatives as Unknowns.
Second Derivatives as Unknowns.
Periodic Exponential Spline Interpolants.
Shape Preservation and Other Considerations.
Spline Interpolation and Smoothing in the Plane.
nterpolation with Arbitrary Splines.
Smoothing with Cubic Spline Interpolants.
Postscript.
A. Appendix.
В. List of Subroutines.
Bibliography.
ndex.
Library of Congress Cataloging-in-Publication Data.
Our intention is to provide an elementary and directly applicable introduction to the computation of those (as simple as possible) spline functions, which are determined by the requirement of smooth and shape-preserving interpolation and (in two cases) the smoothing of measured or collected data.
Contents:
Preface.
Polynomial Interpolation.
The Lagrange Form of the Interpolating Polynomial.
The Newton Form of the Interpolating Polynomial.
Polygonal Paths as Linear Spline Interpolants.
General Spline Interpolants.
arious Representations of a Polygonal Path.
Evaluation by Searching an Ordered List.
Properties of Polygonal Paths.
When the Knots and Interpolation Nodes Are Different.
Parametric Polygonal Paths.
Smoothing with Polygonal Paths I.
Smoothing with Polygonal Paths II.
Quadratic Spline Interpolants.
Knots the Same as Nodes.
Optimal Initial Slope.
Periodic Quadratic Spline Interpolants with Knots the Same as Nodes.
Knots at the Midpoints of the Nodes.
Knots Variable between the Nodes.
Periodic Quadratic Spline Interpolants with Variable Knots between the Nodes.
Nodes Variable between Knots.
Quadratic Histosplines.
Quadratic Hermite Spline Interpolants.
Approximation of First Derivative Values I.
Shape Preservation through the Choice of Additional Knots.
Quadratic Splines with Given Slopes at Intermediate Points.
Cubic Spline Interpolants.
First Derivatives as Unknowns.
Second Derivatives as Unknowns.
Periodic Cubic Spline Interpolants.
Properties of Cubic Spline Interpolants.
First Derivatives Prescribed.
Second Derivatives Prescribed.
Smoothing with Cubic Spline Functions.
Smoothing with Periodic Cubic Spline Functions.
Cubic X-Spline Interpolants.
Discrete Cubic Spline Interpolants.
Local Cubic Hermite Spline Interpolants.
Approximation of Values for the First Derivative II.
Polynomial Spline Interpolants of Degree Five and Higher.
Spline Interpolants of Degree Five.
Quintic Hermite Spline Interpolants where First Derivative Values Are Specified.
Periodic Quintic Hermite Spline Interpolants.
Quintic Hermite Spline Interpolants where Second Derivatives also Are Specified.
Quartic Histosplines.
Higher-Degree Spline Interpolants.
Rational Spline Interpolants.
Rational Splines with One Freely Varying Pole.
Adaptive Rational Spline Interpolants.
Rational Spline Interpolants with a Prescribable Pole.
Rational Spline Interpolants with Two Prescribable Real Poles.
Periodic Rational Spline Interpolants with Two Prescribable Real Poles.
Rational Spline Interpolants with Two Prescribable Real or Complex Poles.
Shape Preservation of Monotone Data.
Shape Preservation of Convex or Concave Data.
Rational Histosplines.
Exponential Spline Interpolants.
First Derivatives as Unknowns.
Second Derivatives as Unknowns.
Periodic Exponential Spline Interpolants.
Shape Preservation and Other Considerations.
Spline Interpolation and Smoothing in the Plane.
nterpolation with Arbitrary Splines.
Smoothing with Cubic Spline Interpolants.
Postscript.
A. Appendix.
В. List of Subroutines.
Bibliography.
ndex.