... cancellations
will occur during the solution. In fact, the preceding item can be viewed
as the special case where the loss of significance is unfortunately total.
Much of the sophistication of complicated linear ... NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
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... special cases where QR is the method of choice.
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Chapter 2. SolutionofLinear Algebraic Equations
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Copyright (C) 1988-1992 by Cambridge ... Backsubstitution
41
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which (peeling of the C
−1
’s one at a time) implies a solution
x = C
1
· C
2
· C
3
···b (2.1.8)
Notice the essential difference between equation...
... stability of Crout’s
50
Chapter 2. SolutionofLinear Algebraic Equations
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Chapter 2. SolutionofLinear Algebraic Equations
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... a[i][j-1]=a[i][j]-dum*a[k][j];
a[i][mm]=0.0;
}
}
}
52
Chapter 2. SolutionofLinear Algebraic Equations
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Copyright (C) 1988-1992 by Cambridge ... a[i][j]*x[j+k];
}
}
54
Chapter 2. SolutionofLinear Algebraic Equations
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Copyright (C) 1988-1992 by Cambridge ... Press),
Đ
4.3.
50
Chapter 2. SolutionofLinear Algebraic Equations
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... 104
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Copyright (C) 1988-1992 by Cambridge ... 2.496 can be achieved — theoretically!]
2.11 Is Matrix Inversion an
N
3
Process?
103
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in terms of which
c
11
= Q
1
+ Q
4
− Q
5
+ Q
7
c
21
= Q
2
+ Q
4
c
12
= Q
3
+...
... enough; but a second
call to verify convergence can be reassuring.
58
Chapter 2. SolutionofLinear Algebraic Equations
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Permission...
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68
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... is cyclic if ∃ an element of G which generates G.
Theorem If G is cyclic and H is a subgroup of G, then H is cyclic.
Proof Suppose G = {a
i
: i ∈ Z} is a cyclic group and H is a subgroup
of G. ... on the concept
of function, and the properties of surjective, injective, and bijective. The notion of a
solution of an equation is central in mathematics, and most properties of functions
can be ... Q is countable but the following three collections are not.
i) P(N), the collection of all subsets of N.
ii) {0, 1}
N
, the collection of all functions f : N → {0, 1}.
iii) The collection of all...
... 92
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