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Volume 2:
Seminumerical Algorithms
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Third Edition
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Juan Marín Noguera
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\begin_inset Quotes eld
\end_inset
..
\begin_inset Quotes erd
\end_inset
*1(1DIGIT *DIGIT)
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\begin_layout Plain Layout
base = atom /
\begin_inset Quotes eld
\end_inset
(
\begin_inset Quotes eld
\end_inset
progress
\begin_inset Quotes eld
\end_inset
)
\begin_inset Quotes erd
\end_inset
\end_layout
\begin_layout Plain Layout
intersection = atom / intersection
\begin_inset Quotes eld
\end_inset
*
\begin_inset Quotes erd
\end_inset
atom
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\begin_layout Plain Layout
progress = intersection / progress (
\begin_inset Quotes eld
\end_inset
+
\begin_inset Quotes erd
\end_inset
/
\begin_inset Quotes erd
\end_inset
-
\begin_inset Quotes erd
\end_inset
) intersection
\end_layout
\end_inset
\end_layout
\begin_layout Plain Layout
An
\family typewriter
atom
\family default
represents all/recommended exercises,
optionally excluding M or HM/excluding HM,
and up to the given difficulty level/all difficulty levels,
or else a single exercise with the given number,
or a range of exercises (both ends inclusive).
Then
\family typewriter
*
\family default
is used for intersection,
\family typewriter
+
\family default
for union,
and
\family typewriter
-
\family default
for set difference.
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\begin_inset ERT
status open
\begin_layout Plain Layout
\backslash
setcounter{chapter}{2}
\end_layout
\end_inset
\end_layout
\begin_layout Chapter
Random Numbers
\end_layout
\begin_layout Section
Introduction
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "3.1.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25+16
\end_layout
\end_inset
\end_layout
\begin_layout Section
Generating Uniform Random Numbers
\end_layout
\begin_layout Subsection
The Linear Congruential Method
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "3.2.1.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25
\end_layout
\end_inset
\end_layout
\begin_layout Subsubsection
Choice of modulus
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "3.2.1.1.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25
\end_layout
\end_inset
\end_layout
\begin_layout Subsubsection
Choice of multiplier
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "3.2.1.2.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25
\end_layout
\end_inset
\end_layout
\begin_layout Subsubsection
Potency
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "3.2.1.3.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Other Methods
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "3.2.2.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25
\end_layout
\end_inset
\end_layout
\begin_layout Section
Statistical Tests
\end_layout
\begin_layout Subsection
General Test Procedures for Studying Random Data
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "3.3.1.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Empirical Tests
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LatexCommand input
filename "3.3.2.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Theoretical Tests
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "3.3.3.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
The Spectral Test
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "3.3.4.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25
\end_layout
\end_inset
\end_layout
\begin_layout Section
Other Types of Random Quantities
\end_layout
\begin_layout Subsection
Numerical Distributions
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "3.4.1.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Random Sampling and Shuffling
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "3.4.2.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25-16
\end_layout
\end_inset
\end_layout
\begin_layout Section
What Is a Random Sequence?
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "3.5.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25
\end_layout
\end_inset
\end_layout
\begin_layout Section
Summary
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "3.6.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25
\end_layout
\end_inset
\end_layout
\begin_layout Chapter
Arithmetic
\end_layout
\begin_layout Section
Positional Number Systems
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "4.1.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25
\end_layout
\end_inset
\end_layout
\begin_layout Section
Floating Point Arithmetic
\end_layout
\begin_layout Subsection
Single-Precision Calculations
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "4.2.1.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Accuracy of Floating Point Arithmetic
\end_layout
\begin_layout Standard
\begin_inset CommandInset include
LatexCommand input
filename "4.2.2.lyx"
literal "false"
\end_inset
\begin_inset Note Note
status open
\begin_layout Plain Layout
\family typewriter
A10+R25
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Double-Precision Calculations
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
7+0;
5 (0:28) -> 3d,
-1/3
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Distribution of Floating Point Numbers
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
10+2;
5,
13,
17 (0:58) -> 5d
\end_layout
\end_inset
\end_layout
\begin_layout Section
Multiple-Precision Arithmetic
\end_layout
\begin_layout Subsection
The Classical Algorithms
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
16+4;
6,
9,
11,
14,
16,
19,
21,
22,
30,
37,
43 (2:58) -> 12d,
-2/3
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Modular Arithmetic
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
8+1;
5,
7,
12,
13 (1:13) -> 4d
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
How Fast Can We Multiply?
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
22+3;
16,
19 (0:56) -> 10d,
-2/3
\end_layout
\end_inset
\end_layout
\begin_layout Section
Radix Conversion
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
9+2;
1,
3,
12,
13,
19 (2:22) -> 8d,
-2/3
\end_layout
\end_inset
\end_layout
\begin_layout Section
Rational Arithmetic
\end_layout
\begin_layout Subsection
Fractions
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
3+1;
5,
6,
8 (0:42) -> 2d,
-2/3
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
The Greatest Common Divisor
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
19+4;
8,
10,
14,
16,
17,
18,
23,
40 (3:19) -> 13d,
-1/3
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Analysis of Euclid's Algorithm
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
17+6;
1,
17,
39,
50 (1:42) -> 9d,
-2/3
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Factoring into Primes
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
32+6;
1,
8,
18,
19,
24,
26,
32,
35 (3:17) -> 17d
\end_layout
\end_inset
\end_layout
\begin_layout Section
Polynomial Arithmetic
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
2+0;
1,
4,
5 (0:31) -> 2d,
-1/3
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Division of Polynomials
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
15+4;
1,
3,
7,
8,
12,
16,
18 (2:08) -> 9d,
-1/3
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Factorization of Polynomials
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
17+5;
1,
2,
10,
12,
18,
22,
34,
40 (3:22) -> 13d,
-2/3
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Evaluation of Powers
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
21+4;
3,
5,
9,
10,
12,
24,
26,
36,
39,
40 (3:37) -> 14d,
-2/3
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Evaluation of Polynomials
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
29+10;
2,
19,
20,
24,
26,
29,
33,
35,
44,
45,
49,
51,
70 (5:24) -> 20d
\end_layout
\end_inset
\end_layout
\begin_layout Section
Manipulation of Power Series
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
8+5;
1,
4,
5,
6,
8,
11,
17 (1:59) -> 7d,
-1/3
\end_layout
\end_inset
\end_layout
\end_body
\end_document
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