## Numerical Methods of Curve FittingFirst published in 1961, this book provides information on the methods of treating series of observations, the field covered embraces portions of both statistics and numerical analysis. Originally intended as an introduction to the topic aimed at students and graduates in physics, the types of observation discussed reflect the standard routine work of the time in the physical sciences. The text partly reflects an aim to offer a better balance between theory and practice, reversing the tendency of books on numerical analysis to omit numerical examples illustrating the applications of the methods. This book will be of value to anyone with an interest in the theoretical development of its field. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

for concordance p 15 1 5 4 Example p 16 1 5 5 The combining of dis | 18 |

inverse Fourier transform p 22 1 7 3 Linear sum of independent variables | 24 |

values p | 33 |

The estimated variance p 41 2 5 4 Testing of estimated standard devia | 41 |

Some Statistical Tests | 48 |

Discrete Distributions | 65 |

being limited to integral values p 74 4 5 4 The sum of two Poisson variables | 75 |

Regression Curves and Functional Relationship | 83 |

7 8 2 4 Direct calculation of values at missed points p | 223 |

Standard Deviations of the Estimates | 249 |

8 2 2 3 Analysis of variance table p 259 8 2 3 Test for homo | 259 |

8 4 2 The use of the tables p 266 8 4 2 1 Example p | 266 |

parameters K2 and K3 p 270 8 5 2 1 Example p 271 8 5 2 2 Range | 274 |

The Grouping of Observations | 287 |

of the standard deviation of an observation p 292 9 1 5 1 Relation | 293 |

9 2 3 The polynomial coefficients p 298 9 2 4 The ﬁtted values | 299 |

5 3 2 Weights p 88 5 3 3 Prediction p | 89 |

The Straight Line | 96 |

value with location of point p 100 6 1 5 1 Example p 102 6 1 6 | 103 |

6 2 3 Example p 107 6 2 4 Tests for homogeneity p | 108 |

for unequallyspaced observations p 123 6 4 3 1 Estimation of ﬁtted | 128 |

Estimation of the Polynomial Coeﬂicients | 147 |

scheme p | 163 |

orthogonal polynomials p 165 7 2 3 Example p 169 7 2 4 The square | 174 |

omitted points p | 183 |

7 5 4 The method of steepest descent p 190 7 5 4 1 Example | 191 |

moments p 194 7 6 2 1 Examplen even p 194 7 6 2 2 Example | 206 |

of the orthogonal polynomial values p 213 7 7 3 Recurrence relations | 214 |

of the estimates p 304 9 4 2 1 Checking for bias before grouping p | 305 |

nomial p 310 9 5 3 Tables of step functions p 310 9 5 4 Example | 313 |

Functions which are not Polynomials | 329 |

functions p 337 10 2 3 2 Example p | 338 |

10 3 3 Harmonic curve through all the points p 343 10 3 4 | 347 |

10 4 4 Summation formulae p 352 10 4 4 1 Example p | 353 |

General Regression and Functional Relationship | 360 |

11 3 2 1 Example p 374 11 3 2 2 The residuals p 374 11 3 3 | 378 |

functions p | 385 |

410 | |

### Other editions - View all

### Common terms and phrases

approximation Biometrika calculating scheme characteristic function Check coefﬁcients coeﬂicients column constant correlation corresponding cubic curve deﬁned degree distributed as X2 Doolittle scheme efﬁciency elements equal error-free estimated standard deviation evaluated Example Table Factors removed ﬁgures ﬁnal ﬁnd ﬁrst ﬁtted curve ﬁtted values ﬁtting formula frequency function functional relationship given in Table gives groups Hence independent variable inverse matrix K2 and K3 linear function listed in Table multiplied normal equations number of observations observed values orthogonal polynomials parameters points of observation Poisson Poisson distribution population mean power-series probability of obtaining quantities range ratio regression curve regression line residuals signiﬁcance level Single-step functions slope solution square root standard deviation Statist step functions straight line subject to error Subtract third-degree tion true value unbiased estimate uniform spacing unity values obtained vanishes variance variation weighted mean zero