Numerical Analysis
Errors in numerical computations are due to a) errors in input data, b) round-off errors, due to the use of a finite number of digits, c) truncation errors, due to approximations, d) mistakes in numerical computations.
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Glossary of functions sec. 2.1 2.1 "JX n(x) 2.2 x!' 5.3 if, e'" = exp(x) 5.3 alogx 5.3 Inx 5.3 sinh x 5.3 coshx 5.3 5.3 tanh x cothx 5.3 arsinhx=sinh-1x 5.3 arcosh x= cosh-I x 5.3 artanhx=tanh-Ix 5.3 arcoth X= coth-I x 5.3 sinx 5.4 5.4 cosx 5.4 tan x cotx 5.4 secx 5.4 cscx 5.4 arcsinx= sin-Ix 5.4 arccos x = cos-I x 5.4 arctan x = tan-I x 5.4 Ixl
arccotx=coC1x F(a, b, c, x) F(b, c, x) Pn(x) P,;?(x) Tn(x), Tntx) Un(x), untx) Hn(x) hn(x) LI/(x) Ln(a)(x) II/(x) Pn(a,fJ)(x) Bn(x) En(x) Jp(x) Yp(x) H~l) (x) H~2) (x)
[n(x) KI/(x)
Ber(x) Bei(x) Ker(x)
544
5.4 9.2 9.2 12.2 12.2 12.2 12.2 12.2 12.2 12.2 12.2 12.2 12.2 12.3 12.3, 12.5 12.4 12.4 12.4 12.4 12.4 12.4 12.4 12.4 12.4
Kei(x) r(x) B(p, q) F(k, cp) E(k, cp) nCk, n, cp) K(k) E(k)
Ei(x) li(x) erf(x) erfc(x) Si(x) Ci(x) C(x) Sex) B(t) sgn(t) oCt) cp(x)
11> (x)
12.4 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.5 12.6 12.6 12.6 17.2 17.8
19
Glossary of symbols Symbol
Meaning
Section
and
1.1
v
or
1.1
V
exclusive or
1.1
negation
1.1
implies
1.1
equivalent
1.1
there exists
1.1
for all
1.1
NAND
1.1
NOR
1.1
thus belongs to
1.2
c
subset
1.2
superset
1.2
c
complement
1.2
n
intersection
1.2
u
union
1.2
\
E
difference
1.2
~
symmetric difference difference Laplacian
1.2 6.1,6.3 11.2
x
product set
1.2
o
empty set
1.2
Df,Rf
domain, range off
1.3
binomial coefficient
2.1
CD
N,Z,Q,R,C Rn
number sets
2.2
Euclidean space
10.1
Zn
set of congruence classes modulo n
1.4
Z2 n
set of binary n-tuples
1.6
F[x]
polynomial ring over field F
1.4
as, S
boundary, closure of S
4.7, 10.1
U'v, uTv, (u, v), (ulv), u*v
scalar product
3.4,4.1,4.7,12.7,4.10
u xv
vector product
3.4
lui lIull,llullm,p
length (norm)
3.4,4.7
norm
12.7, 12.8
A=(aij)' [aij]
matrix
4.1
545
19 [A]ij=aij AT
element of matrix transpose of matrix
4.1
A*
adjoint of matrix
4.10
IIAII
norm of matrix
, dy D . _dy y = dx = y, Y - dt
~
derivative
16.3 6.3
partial derivative
10.4
f:
directional derivative
10.4
a an
normal derivative
11.4
d(Yl' ... , Yn) d(X 1, ... , xn)
Jacobian determinant
10.6
V
gradient
11.2
f;=fx=
E, fl, V, 0, .u
difference operators
16.4
LP
Lebesgue spaces
12.8
em
spaces of differentiable functions
12.8
Wm,p,H m
Sobolev spaces
12.8
O( ),o( )
ordo
8.5
[,],(,)
closed, open interval
6.1
row equivalence asymptotic equivalence
4.1 8.5
*
convolution
12.8
equality
*< (::;;)
inequality
> (;:::)
greater than (or equal)
-
identity
less than (or equal)
approximately equal
-
congruent to
II
parallel to
..1
perpendicular to
0kn=
I, II
{I,
k=n O,k*-n
infinity Kronecker delta factorial, semifactorial
546
2.1
Index
ANOVA, analysis of variance 509
ARMA-process 442 AR-process 442 Abbreviations in computer science 534 Abel's limit theorem 188 Abel's test 186 Abelian group 22, 25 Absolute error 391 Absolute value 46 Acceleration 246 Acceptance sampling control 519 Acceptance-rejection method for simulation 448 Accumulation point 221,2
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