Tài liệu Solution of Linear Algebraic Equations part 11 ppt
Tài liệu Solution of Linear Algebraic Equations part 11 ppt
... 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 Equations
Sample ... 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 Alg...
Tài liệu Solution of Linear Algebraic Equations part 2 ppt
... case of N × N matrices, with M sets of right-hand
side vectors, in completely analogous fashion. The routine implemented below
is, of course, general.
38
Chapter 2. Solution of Linear Algebraic Equations
Sample ... Moler, C.B. 1967,
Computer Solution of Linear Algebraic Systems
(Engle-
wood Cliffs, NJ: Prentice-Hall).
Wilkinson, J.H., and Reinsch, C. 1971,
Linear Alg...
Tài liệu Solution of Linear Algebraic Equations part 6 pptx
... improved solution x.
2.5 Iterative Improvement of a Solution to
Linear Equations
Obviously it is not easy to obtain greater precision for the solution of a linear
set than the precision of your ... 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 (IS...
Tài liệu Solution of Linear Algebraic Equations part 1 docx
... 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
+ ···+a
1N
x
N
=b
1
a
21
x
1
+ ... equations as unknowns, and there is a good
chance of solving for a unique solution set of x
j
’s. Analytically, there can fail to
be a u...
Tài liệu Solution of Linear Algebraic Equations part 3 pdf
... 42
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
Copyright ... is called backsubstitution.Thecom-
bination of Gaussian elimination and backsubstitution yields a solution to the set
of equations.
The advantage of Gaussian elimination and backsubstitutionover ... York:
McGraw-...
Tài liệu Solution of Linear Algebraic Equations part 4 docx
... 1967,
Computer Solution of Linear Algebraic Systems
(Engle-
wood Cliffs, NJ: Prentice-Hall), Chapters 9, 16, and 18.
Westlake, J.R. 1968,
A Handbook of Numerical Matrix Inversion and Solution of Linear Equations
(New ... (i.e., selection of a salubrious pivot element
for the division in equation 2.3.13) is absolutely essential for the stability of Crout’s
50
Chapter 2....
Tài liệu Solution of Linear Algebraic Equations part 5 docx
... 1967,
Computer Solution of Linear Algebraic Systems
(Engle-
wood Cliffs, NJ: Prentice-Hall), Chapters 9, 16, and 18.
Westlake, J.R. 1968,
A Handbook of Numerical Matrix Inversion and Solution of Linear Equations
(New ... (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 RECI...
Tài liệu Solution of Linear Algebraic Equations part 12 pdf
... 104
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
Copyright ... terms of which
c
11
= Q
1
+ Q
4
− Q
5
+ Q
7
c
21
= Q
2
+ Q
4
c
12
= Q
3
+ Q
5
c
22
= Q
1
+ Q
3
− Q
2
+ Q
6
(2 .11. 4)
What’s the use of this? There is one fewer multiplication than in equation
(2 .11. 2), ... in (2...
Tài liệu Solution of Linear Algebraic Equations part 7 docx
... North America).
A
⋅
x = b
SVD solution
of A
⋅
x = c
solutions of
A
⋅
x = c′
solutions of
A
⋅
x = d
null
space
of A
SVD solution of
A
⋅
x = d
range of A
d
c
(b)
(a)
A
x
b
c′
Figure ... making
the same permutation of the columns of U,elementsofW,andcolumnsofV(or
rows of V
T
), or (ii) forming linear combinations of any columns of U and V whose
correspo...
Tài liệu Solution of Linear Algebraic Equations part 8 docx
... case of a tridiagonal matrix was treated 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 ... also be aware of some of the special sparse forms that occur in the
solutionof partial differential equations in two or more dimensions. See Chapter 19.
If your particular patt...