cliffs quick review linear algebra
Tài liệu Solution of Linear Algebraic Equations part 1 docx
Ngày tải lên :
15/12/2013, 04:15
... trade@cup.cam.ac.uk (outside North America).
Chapter 2. Solution of Linear
Algebraic Equations
2.0 Introduction
A set of linear algebraic equations looks like this:
a
11
x
1
+ a
12
x
2
+ a
13
x
3
+ ... wrong:
ã While not exact linear combinations of each other, some of the equations
may be so close to linearly dependent that roundoff errors in the machine
render them linearly dependent at some ... storage
scheme, “pointer to array of pointersto rows.” You might wish to review that section
34
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART...
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Tài liệu Solution of Linear Algebraic Equations part 2 ppt
Ngày tải lên :
15/12/2013, 04:15
... Moler, C.B. 1967,
Computer Solution of Linear Algebraic Systems
(Engle-
wood Cliffs, NJ: Prentice-Hall).
Wilkinson, J.H., and Reinsch, C. 1971,
Linear Algebra
,vol.IIof
Handbook for Automatic ... 36
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... analogous fashion. The routine implemented below
is, of course, general.
38
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING...
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Tài liệu Solution of Linear Algebraic Equations part 11 ppt
Ngày tải lên :
15/12/2013, 04:15
... Reinsch, C. 1971,
Linear Algebra
,vol.IIof
Handbook for Automatic Com-
putation
(New York: Springer-Verlag), Chapter I/1.
Gill, P.E., Murray, W., and Wright, M.H. 1991,
Numerical Linear Algebra and ... to solve linear systems. In many applications only the
part (2.10.4) of the algorithm is needed, so we separate it off into its own routine rsolv.
98
Chapter 2. Solution of Linear Algebraic ... is not used for typical systems of linear equations. However, we will
meet special cases where QR is the method of choice.
100
Chapter 2. Solution of Linear Algebraic Equations
Sample page from...
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Tài liệu Solution of Linear Algebraic Equations part 3 pdf
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24/12/2013, 12:16
... 42
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... for
example in support of full pivoting.
CITED REFERENCES AND FURTHER READING:
Wilkinson, J.H. 1965,
The Algebraic Eigenvalue Problem
(New York:Oxford University Press). [1]
Carnahan, B., Luther, H.A., ... Program B-2, p. 298.
Westlake, J.R. 1968,
A Handbook of Numerical Matrix Inversion and Solution of Linear Equations
(New York: Wiley).
Ralston, A., and Rabinowitz, P. 1978,
A First Course in Numerical...
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Tài liệu Solution of Linear Algebraic Equations part 4 docx
Ngày tải lên :
24/12/2013, 12:16
... Mathematical
Computations
(Englewood Cliffs, NJ: Prentice-Hall),
Đ
3.3, and p. 50.
Forsythe, G.E., and Moler, C.B. 1967,
Computer Solution of Linear Algebraic Systems
(Engle-
wood Cliffs, NJ: Prentice-Hall), ... i = j +1 N
of equation (2.3.13).sum=a[i][j];
for (k=1;k<j;k++)
44
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... solve the linear set
A · x =(L·U)·x=L·(U·x)=b (2.3.3)
by first solving for the vector y such that
L · y = b (2.3.4)
and then solving
U · x = y (2.3.5)
What is the advantage of breaking up one linear...
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Tài liệu Solution of Linear Algebraic Equations part 5 docx
Ngày tải lên :
24/12/2013, 12:16
... Mathematical
Computations
(Englewood Cliffs, NJ: Prentice-Hall),
Đ
3.3, and p. 50.
Forsythe, G.E., and Moler, C.B. 1967,
Computer Solution of Linear Algebraic Systems
(Engle-
wood Cliffs, NJ: Prentice-Hall), ... {
k=i-m1-1;
tmploop=LMIN(m1+m2+1,n-k);
b[i]=0.0;
for (j=LMAX(1,1-k);j<=tmploop;j++) b[i] += a[i][j]*x[j+k];
}
}
54
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... Numerical Analysis
, 2nd ed. (New York:
McGraw-Hill),
Đ
9.11.
Wilkinson, J.H., and Reinsch, C. 1971,
Linear Algebra
,vol.IIof
Handbook for Automatic Com-
putation
(New York: Springer-Verlag), Chapter...
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- 0
Tài liệu Solution of Linear Algebraic Equations part 12 pdf
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24/12/2013, 12:16
... 104
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... 1987,
Algorithms: Their Complexity and Efciency
, 2nd ed. (New York: Wiley).
Winograd, S. 1971,
Linear Algebra and Its Applications
, vol. 4, pp. 381–388.
Pan, V. Ya. 1980,
SIAM Journal on Computing
, ... Faster
, Lecture Notes in Computer Science, vol. 179
(New York: Springer-Verlag)
Pan, V. 1984,
SIAM Review
, vol. 26, pp. 393–415. [More recent results that show that an
exponent of 2.496 can be achieved...
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Tài liệu Solution of Linear Algebraic Equations part 6 pptx
Ngày tải lên :
24/12/2013, 12:16
... 1974,
Numerical Methods
(Englewood Cliffs, NJ: Prentice-Hall),
Đ
5.5.6, p. 183.
Forsythe, G.E., and Moler, C.B. 1967,
Computer Solution of Linear Algebraic Systems
(Engle-
wood Cliffs, NJ: Prentice-Hall), ... enough; but a second
call to verify convergence can be reassuring.
58
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... 56
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING...
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Tài liệu Solution of Linear Algebraic Equations part 7 docx
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24/12/2013, 12:16
... Sparse Linear Systems
A system of linear equations is called sparse if only a relatively small number
of its matrix elements a
ij
are nonzero. It is wasteful to use general methods of
linear algebra ... *g;
g=s=scale=0.0;
if(i<=m&&i!=n){
for (k=l;k<=n;k++) scale += fabs(a[i][k]);
if (scale) {
62
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... b
=0, q.e.d.
Figure 2.6.1 summarizes our discussion of SVD thus far.
68
Chapter 2. Solution of Linear Algebraic Equations
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Tài liệu Solution of Linear Algebraic Equations part 8 docx
Ngày tải lên :
24/12/2013, 12:16
... Sparse Linear Systems
A system of linear equations is called sparse if only a relatively small number
of its matrix elements a
ij
are nonzero. It is wasteful to use general methods of
linear algebra ... specially, because that
particular type of linear system admits a solution in only of order N operations,
rather than of order N
3
for the general linear problem. When such particular types
exist, ... routine sprstp before
sending it to the matrix multiply routine.
86
Chapter 2. Solution of Linear Algebraic Equations
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Tài liệu An introduction to Linear Algebra pdf
Ngày tải lên :
17/01/2014, 04:20
... of linear algebra used in most chemometric methods. Readers who are somewhat
familiar with linear algebra may find this article to be a good quick review. Those totally
unfamiliar with linear algebra ... understand most
chemometric techniques without a basic understanding of linear algebra. This article
reviews the basics of linear algebra and provides the reader with the foundation required for
understanding ... the vectors are linearly independent. Otherwise, at least one of the vectors is a linear
combination of the other vectors and they are linearly dependent.
It is easy to visualize linear independence....
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Tài liệu Elements of abstract and linear algebra docx
Ngày tải lên :
17/01/2014, 04:20
... after the
first four chapters, the linear algebra follows easily. Finishing the chapter on linear
algebra gives a basic one year undergraduate course in abstract algebra. Chapter 6
continues the ... S. However the ordering may be linear on S but not linear on A. The HMP is
that any linearly ordered subset of a partially ordered set is contained in a maximal
linearly ordered subset.
Exercise ... included. There are three
good reasons for this. First, linear algebra has top priority. It is better to go
forward and do more linear algebra than to stop and do more group and ring
theory....
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Tài liệu Linear Algebra Done Right_ Second Edition doc
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17/01/2014, 04:20
... spaces: span, linear independence,
basis, and dimension.
Let’s review our standing assumptions:
Recall that F denotes R or C.
Recall also that V is a vector space over F.
✽✽
21
Linear Algebra
Done ... the many mathematicians who cre-
ated linear algebra during the last two centuries. In writing this book I
tried to think about the best way to present linear algebra and to prove
its theorems, ... abstract vector spaces
and linear maps.
The audacious title of this book deserves an explanation. Almost
all linear algebra books use determinants to prove that every linear op-
erator on a finite-dimensional...
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Tài liệu PROBLEMS AND THEOREMS IN LINEAR ALGEBRA pdf
Ngày tải lên :
17/01/2014, 04:20
... with main notions of linear algebra:
linear space, basis, linear map, the determinant of a matrix. Apart from that,
all the essential theorems of the standard course of linear algebra are given ... most attractive problems and theorems of linear
algebra still accessible to first year students majoring or minoring in mathematics.
The computational algebra was left somewhat aside. The major ... Theorem. Let T : V −→ V be a linear operator such that the
vectors ξ, T ξ, . . . , T
n
ξ are linearly dependent for every ξ ∈ V . Then the
operators I, T, . . . , T
n
are linearly dependent.
Problems
8....
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