Numerical Methods of Curve FittingCambridge University Press, 13 de des. 2012 - 438 pàgines 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. |
Continguts
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 |
Regression Curves and Functional Relationship | 83 |
5 3 2 Weights p 88 5 3 3 Prediction p | 89 |
page | 95 |
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 |
and к р 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 |
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 |
of observations p 112 6 3 3 Example p 113 6 3 4 The estimation | 116 |
for unequallyspaced observations p 123 6 4 3 1 Estimation of fitted | 128 |
ship p 129 6 5 2 1 Estimates of the slope p 130 6 5 2 2 Ratio of standard | 138 |
Estimation of the Polynomial Coefficients | 147 |
method p 153 7 1 4 The abbreviated Doolittle method p 155 7 1 5 | 159 |
orthogonal polynomials p 165 7 2 3 Example p 169 7 2 4 The square | 174 |
Discrete Distributions | 179 |
omitted points p | 183 |
7 5 4 The method of steepest descent p 190 7 5 4 1 Example | 191 |
orthogonal moments p 201 7 6 3 1 Tables of orthogonal polynomials | 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 |
Example p 362 11 1 4 Orthogonal functions p 363 11 1 5 Significance | 366 |
11 3 2 1 Example p 374 11 3 2 2 The residuals p 374 11 3 3 | 378 |
functions p | 385 |
viscosity of water with temperature | 396 |
Bibliography | 405 |
Altres edicions - Mostra-ho tot
Frases i termes més freqüents
a₁ abbreviated Doolittle approximation b₁ b₁x b₁y Biometrika characteristic function coefficients constant corresponding cubic curve degree distributed as x² Doolittle scheme efficiency elements equal equally-spaced error-free evaluated Factors removed fitted curve fitted values formula frequency function functional relationship gives groups Hence independent variable interval inverse matrix K₂ least-squares estimate M₁ multiplied normal equations number of observations observed values orthogonal polynomials parameters points of observation Poisson distribution probability of obtaining quantities range ratio recurrence relation regression curve regression line residuals significance level Single-step functions slope solution standard deviation Statist step function method step functions straight line subject to error Subtract tion true value unbiased estimate unity v₁ values obtained variance W₁ weighted mean Y₁ zero Σ Σ σ² Συ Συλ Σχ Σω