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| Scarborough J.B. — Numerical Mathematical Analysis |
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| Предметный указатель |
Remainder term, in Gauss's formula 167
Remainder term, in Lagrange's formula 85 91
Remainder term, in Newton's formula (I) 86 90
Remainder term, in Newton's formula (II) 87 90
Remainder term, in Simpson's rule 154—159 161
Remainder term, in Stirling's formula 88 90
Remainder term, in Weddle's rule 155
Residuals 308
Residuals of plotted points 357
Residuals, law of error for 310
Residuals, sum of 309
Residuals, theorem concerning 309
Residuals, weighted, of a function 370
Root-squaring process, principle of 198
Root-squaring process, rule for applying 200 201
Root-squaring process, when to discontinue 203
Roots, complex, detection of 206
Roots, computation of, by iteration 184 191
Roots, computation of, by Newton — Raphson method 178 187
Roots, computation of, by regula falsi method 174
Roots, finding approximate values of 171
Roots, Graeffe's method for finding 198
Roots, location of 172
Rounding numbers, rule for 2
Runge — Kutta method 273
Runge — Kutta method, applied to simultaneous equations 275
Runge — Kutta method, inherent error in 275
Runge — Kutta method, remarks on 279
Runge — Kutta method, special case of 274
Runge, Carl 396
Scheme for 12 ordinates 396
Scheme for 24 ordinates 401
Series approximations, accuracy of 27
Series, alternating, error in 30
Series, asymptotic 140 298
Series, exponential, remainder term in 31 32
Series, interpolation 84
Series, logarithmic, remainder term in 32
Sets of measurements, combination of, when P.E.'s are given 328
Significant figures 2
Significant figures, in powers, roots, logs, and antilogs 18
Significant figures, in products and quotients 18
| Significant figures, loss of, by subtraction 12
Significant figures, relation of, to relative error 3 6
Simpson's rule 119
Simpson's rule, error due to inaccurate data in 163
Simpson's rule, formulas for error in 156—159 161 162
Simpson's rule, geometric significance of 120
Simpson's three-eighths rule 120
Simpson's three-eighths rule, accuracy of, compared with one-third rule 155
Simultaneous algebraic and transcendental equations, solutions of, by iteration 191
Simultaneous algebraic and transcendental equations, solutions of, by Newton — Raphson method 187
Simultaneous differential equations, solution of, by Runge — Kutta method 275
Simultaneous differential equations, solution of, by successive approximations 232
Standard deviation 323
Stirling's formula of interpolation 60
Stirling's formula of interpolation, as a power series 80
Stirling's formula of interpolation, compared with Bessel's 68 69
Stirling's formula of interpolation, when to use 68 69 91
Substituted polynomials, convergence in case of 260
Subtraction, accuracy of 11
Subtraction, loss of significant figures by 12
Tannery, Jules 2
Target, probability of hitting 299
Taylor's formula 28
Taylor's formula, remainder term in 28
Trapezoidal rule 118
Trapezoidal rule, geometric significance of 119
Trigonometric interpolation 112
Trigonometric series 388
Trigonometric series, case of 12 ordinates 388
Trigonometric series, case of 24 ordinates 398
Uhler, H.S. 380
Value of h for stipulated accuracy in integral 162
Van Orstrand, C.E. 373
Weddle's rule 120
Weddle's rule, geometric significance of 121
Weddle's rule, inherent error in 155
Weierstrass, theorems of 39
Weight and probable error, relation between 323
Weight, definition of 306
Weight, of a function 371
Weighted mean 309
Weighted mean, normal equations, rule for writing down 372
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