# Numerical Methods of Curve Fitting

Cambridge University Press, Dec 13, 2012 - Mathematics - 438 pages
First 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.

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### 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 Bibliography page 410 Copyright