Handbook of Splines

ISBN-13: 9789401062442 / Angielski / Miękka / 2012 / 606 str.

Gheorghe Micula; Sanda Micula

Opis

The numerous publications on spline theory during recent decades show the importance of its development on modern applied mathematics. The purpose of this book is to give a comprehensive approach to the theory of spline functions, from the introduction of the phrase 'spline' by I.J. Schoenberg in 1946 to the newest theories of spline-wavelets or spline-fractals, emphasizing the significance of the relationship between the general theory and its applications. In addition, this volume provides new material on spline function theory, as well as a fresh look at basic methods in spline functions. The authors have complemented the work with an extensive reference section to stimulate further study.

Spis treści

1 Spline Functions and the Representation of Linear Functionals.- 2 Multivariate Spline Functions.- 3 Nonlinear Sets of Spline Functions.- 4 Numerical Treatment of the Integral E-Quations.- 5 Numerical Solution of Ordinary Differential Equations.- 6 Splines and Finite Elements.- 7 Finite Element Method for Solution of Boundary Problems for Partial Differential Equations.- 8 Spline Functions in Computer Aided Geometric Design.- 9 From Spline to Fractals.- 10 Box Splines.- 11 Spline Wavelets.- 12 References.