Numerical Methods of Curve Fitting

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