Tài liệu Evaluation of Functions part 3 pptx
Tài liệu Evaluation of Functions part 3 pptx
... 1970,
Mathematical Methods of Physics
, 2nd ed. (Reading, MA:
W.A. Benjamin/Addison-Wesley),
§
2 .3. [2]
5.2 Evaluation of Continued Fractions
Continued fractions are often powerful ways of evaluating functions ... as good as other methods.
170
Chapter 5. Evaluation of Functions
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)
C...
Tài liệu Evaluation of Functions part 4 pptx
... E are to be precomputed by
A =(a
4
)
1/4
B=
a
3
−A
3
4A
3
D=3B
2
+8B
3
+
a
1
A−2a
2
B
A
2
C =
a
2
A
2
−2B−6B
2
−D
E =a
0
−B
4
−B
2
(C+D)−CD
(5 .3. 3)
... Mathe-
matical Association of America), pp. 1 83, 190. [1]
Mathews, J., and Walker, R.L. 1970,
Mathematical Methods of Physics
, 2nd ed. (Reading, MA:
W.A. Benjamin/Addison-Wesley), pp. 36 1 36 3. [2]
Knuth, ... 1981,
Seminumer...
Tài liệu Evaluation of Functions part 6 pptx
... combination of
J
0
and J
1
, which are of order unity.
180
Chapter 5. Evaluation of Functions
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)
Copyright ... 1991,
Mathematics and Computers in Simulation
, vol. 33 , pp. 33 –49.
Knuth, D.E. 1981,
Seminumerical Algorithms
, 2nd ed., vol. 2 of
The Art of Computer Programming
(Readin...
Tài liệu Evaluation of Functions part 10 pptx
... degree
of approximation (length of
c
to be used), this routine returns the array
cint[0 n-1]
,the
Chebyshev coefficients of the integral of the function whose coefficients are
c
. The constant of
integration ... routine
chebft
§5.8,andgiven
n
, the desired degree
of approximation (length of
c
to be used), this routine returns the array
cder[0 n-1]
,the
Chebyshev coefficients of the...
Tài liệu Integration of Functions part 3 docx
... Cliffs, NJ: Prentice-Hall),
§
5 .3.
138
Chapter 4. Integration of Functions
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)
Copyright (C) 1988-1992 ... term
decreasing as 1/N
3
whichisclosedontherightandopenontheleft:
x
N
x
1
f(x)dx = h
23
12
f
2
+
7
12
f
3
+ f
4
+ f
5
+
···+f
N−2
+
13
12
f
N −1
+
5
12
f
N
+ O
1
N
3
...
Tài liệu Integration of Functions part 6 pptx
... range of integration.
{
int j;
float xr,xm,dx,s;
static float x[]={0.0,0.14887 433 89,0. 433 39 539 41, The abscissas and weights.
First value of each array
not used.
0.6794095682,0.8650 633 666,0.9 739 065285};
static ... power
of the number needed to do a one-dimensional integral. If you need 30 function
evaluations to do a one-dimensional integral crudely, then you will likely need...
Tài liệu Integration of Functions part 7 pptx
... power
of the number needed to do a one-dimensional integral. If you need 30 function
evaluations to do a one-dimensional integral crudely, then you will likely need on
the order of 30 000 evaluations ... Integrals
Integrals of functions of several variables, over regions with dimension greater
than one, are not easy. There are two reasons for this. First, the number of function...
Tài liệu Evaluation of Functions part 2 doc
... large x.
Accelerating the Convergence of Series
There are several tricks for accelerating the rate of convergence of a series (or,
equivalently, of a sequence of partial sums). These tricks will not ... Similarly, the form of the coefficients a is often such as to make
use of previous work: Terms like k! or (2k)! can be updated in a multiply or two.
165
168
Chapter 5. Evaluation...
Tài liệu Evaluation of Functions part 11 pdf
... Mathe-
matical Association of America), pp. 59, 182–1 83 [synthetic division].
5.11 Economization of Power Series
One particular application of Chebyshev methods, the economization of power series,is
an ... 198
Chapter 5. Evaluation of Functions
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)
Copyright (C) 1988-1992 by Cambridge...
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