Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Basics
- 3 Short introduction to Linux
- 4 Interpolation
- 5 Taking derivatives
- 6 Numerical integration
- 7 Solution of nonlinear equations
- 8 Differential equations
- 9 Matrices
- 10 Random processes and Monte Carlo simulation
- References
- Appendix A The ROOT system
- Appendix B Free scientific libraries
- Appendix C FORTRAN and C++
- Appendix D Program listings
- Index
4 - Interpolation
Published online by Cambridge University Press: 04 August 2010
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Basics
- 3 Short introduction to Linux
- 4 Interpolation
- 5 Taking derivatives
- 6 Numerical integration
- 7 Solution of nonlinear equations
- 8 Differential equations
- 9 Matrices
- 10 Random processes and Monte Carlo simulation
- References
- Appendix A The ROOT system
- Appendix B Free scientific libraries
- Appendix C FORTRAN and C++
- Appendix D Program listings
- Index
Summary
An important part in a scientist's life is the interpretation of measured data or theoretical calculations. Usually when you do a measurement you will have a discrete set of points representing your experiment. For simplicity, we assume your experiment to be represented by pairs of values: an independent variable “x,” which you vary and a quantity “y,” which is the measured value at the point x. As an illustration, consider a radioactive source and a detector, which counts the number of decays. In order to determine the half-life of this source, you would count the number of decays N0, N1, N2, …, Nk at times t0, t1, t2, …, tk. In this case t would be your independent variable, which you hopefully would choose in such a way that it is suitable for your problem. However, what you measure is a discrete set of pairs of numbers (tk, Nk) in the range of (t0, tk). In order to extract information from such an experiment, we would like to be able to find an analytical function which would give us N for any arbitrary chosen point t. But, sometimes trying to find an analytical function is impossible, or even though the function might be known, it is too time consuming to calculate or we might be only interested in a small local region of the independent variable.
- Type
- Chapter
- Information
- Introductory Computational Physics , pp. 25 - 36Publisher: Cambridge University PressPrint publication year: 2006