Curve-Fitting: The Science and Art of Approximation

This is a how-to guide on the approximation of data. There are many books and articles on curve-fitting. This is intended as a supplement to, not a replacement for, such texts. Most references are either esoteric or simplistic. I hope to strike a balance between these two extremes and trust you will find this helpful. Many examples are included and all of the source code is available on-line. Foreword Introduction Chapter 1. The Challenge Chapter 2. The Math Chapter 3. The Shape of Functions Chapter 4. The Nature of Data Chapter 5. The Importance of Size Chapter 6. The Importance of Scale Chapter 7. The Importance of Orthogonality Chapter 8. More Orthogonal Functions Chapter 9. Fourier Series Chapter 10. Multivariate Regression Chapter 11. Contours Chapter 12. Four-Dimensional Data Chapter 13. Data Plateau Chapter 15. Lagrange Interpolation Chapter 16. Piecewise Approximation Chapter 17. Cubic Splines Chapter 18. Min/Max Approximation Chapter 19. Parametric Approximation Chapter 20. Approximation by Relaxation Chapter 21. The Inverse Distance Method Chapter 22. Newton's Method Chapter 23. Quasi-Newton Methods Appendix A. High Accuracy Gauss Elimination Appendix B. Linear Least-Squares Solver Appendix C. Linear Least-Squares with Linear Constraints Appendix D. Orthogonal Polynomials Appendix E. Lagrange Interpolation Appendix F. Cubic Splines Appendix G: Relaxation Code Appendix H. Inverse Distance Code Appendix I. Newton's Method Appendix J. Modified Broyden's Method Appendix K. SIAM Paper The Handbook of Mathematical Functions Afterword