数值分析

所属分类:数学  
出版时间:2001-8   出版时间:高等教育出版社   作者:Richard L.Bursen   页数:841   字数:1177000  
Tag标签:数学,数值计算,numerical_analysis,计算机,英文原版,数值分析,计算机科学  

内容概要

  本书介绍了现代数值近似技术的理论及实用知识,解释了它们的工作原理。同它的前几个版本一样,该书仍将重点放在近似技术的数值分析上,以便为读者今后的学习打下坚实的数值分析与科学计算基础。本书内容丰富、翔实,可以根据不同的学习对象和学习目的,选择、组织、串联相应的章节,形成侧重于理论或是侧重于实用的两种学习策略。书中的每个概念均以大量的例子说明,同时书中还包含2000多个习题,范围从方法、算法的基本应用到理论的归纳与扩展,涉及物理、计算机、生物、社会科学等多个不同的领域。通过这些实例,进一步说明在现实世界中,数值方法是如何被应用的。第七版新增了两个突出的部分,一是前承条件共轭梯度方法,为线性方程系统提供了更完备的解决方法;另一部分是同伦与连续方法,为非线性方程系统的近似求解提供了不同的方法。

作者简介

作者:(美国)伯登(Richard L.Burden) J.Douglas Faires

书籍目录

1.
MATHEMATICAL
PRELIMINARIES
1.1
Review
of
Calculus
  1.2
Round-off
Errors
and
Computer
Arithmetic
 1.3
Algorithms
and
Convergence
 1.4
Numerical
Software
2.
SOLUTIONS
OF
EQUATIONS
IN
ONE
VARIABLE
 2.1
The
Bisection
Method
 2.2
Fixed-Point
Iteration
 2.3
The
Newton's
Method
 2.4
Error
Analysis
for
Iterative
Methods
 2.5
Accelerating
Convergence
 2.6
Zeros
of
Polynomials
and
Muller's
Method
 2.7
Survey
of
Methods
and
Software
3.
INTERPOLATION
AND
POLYNOMIAL
APPROXIMATION
 3.1
Interpolation
and
the
LaGrange
Polynomial
 3.2
Divided
Differences
 3.3
Hermite
Interpolation
 3.4
Cubic
Spline
Interpolation
 3.5
Parametric
Curves
 3.6
Survey
of
Methods
and
Software
4.
NUMERICAL
DIFFERENTIATION
AND
INTEGRATION
 4.1
Numerical
Differentiation
 4.2
Richardson's
Extrapolation
 4.3
Elements
of
Numerical
Integration
 4.4
Composite
Numerical
Integration
 4.5
Romberg
Integration
 4.6
Adaptive
Quadrature
Methods
 4.7
Gaussian
Quadrature
 4.8
Multiple
Integrals
 4.9
Improper
Integrals
 4.10
Survey
of
Methods
and
Software
5.
INITIAL-VALUE
PROBLEMS
FOR
ORDINARY
DIFFERENTIAL
EQUATIONS
 5.1
The
Elementary
Theory
of
Initial-Value
Problems
 5.2
Euler's
Method
 5.3
Higher-Order
Taylor
Methods
 5.4
Runge-Kutta
Methods
 5.5
Error
Control
and
the
Runge-Kutta-Fehlberg
Method
 5.6
Multi-Step
Methods
 5.7
Variable
Step-Size
Multi-Step
Methods
 5.8
Extrapolation
Methods
 5.9
Higher-Order
Equations
and
Systems
of
Differential
Equations
 5.10
Stability
 5.11
Stiff
Differential
Equations
 5.12
Survey
of
Methods
and
Software
6.
DIRECT
METHODS
FOR
SOLVING
LINEAR
SYSTEMS
7.
ITERATIVE
TECHNIQUES
IN
MATRIX
ALGEBRA
8.
APPROXIMATION
THEORY
9.
APPROXIMATING
EIGENVALUES
10.
NUMERICAL
SOLUTIONS
OF
NONLINEAR
SYSTEMS
OF
EQUATIONS
11.
BOUNDARY-VALUE
PROBLEMS
FOR
ORDINARY
DIFFERENTIAL
EQUATIONS
12.
NUMERICAL
SOLUTIONS
TO
PARTIAL
DIFFERENTIAL
EQUATIONS
BIBLIOGRAPHY
ANSWERS
TO
SELECTED
EXERCISES
INDEX

章节摘录

版权页:
插图:
Factorizations
take
a
simpler
form
when
the
matrix
A
is
positive
definite.For
example,the
Choleski
factorization
has
the
form
A=LLt,where
L
is
lower
triangular.A
symmetric
matrix
that
has
an
LU
factorization
can
also
be
factored
in
the
form
A
=LDLt,where
D
is
diagonal
and
L
is
lower
triangular
with
1's
on
the
diagonal.With
these
factorizations,marupulations
involving
A
can
be
simplified.If
A
is
tridiagonal,the
LU
factorization
takes
a
particularly
simple
form,with
U
having
1's
on
the
main
diagonal
and
0s
elsewhere,except
on
the
diagonal
immediately
above
the
main
diagonal.In
addition,L
has
its
only
nonzero
entries
on
the
main
diagonal
and
one
diagonal
below.
The
direct
methods
are
the
methods
of
choice
for
most
linear
systems.For
tridiagonal,banded,and
positive
definite
matrices,the
special
methods
are
recommended.For
the
general
case,Gaussian
elimination
or
LU
factorization
methods,which
allow
pivoting,are
recommended.In
these
cases,the
effects
of
roundoff
error
should
be
monitored.In
Section
7.4
we
discuss
estimating
errors
in
direct
methods.
Large
linear
systems
with
primarily
0
entries
occurring
in
regular
patterns
can
be
solved
efficiently
using
an
iterative
procedure
such
as
those
discussed
in
Chapter
7.Systems
of
this
type
arise
naturally,for
example,when
finite-difference
techniques
are
used
to
solve
boundary-value
problems,a
common
application
in
the
numerical
solution
of
partial-differential
equations.
It
can
be
very
difficult
to
solve
a
large
linear
system
that
has
primarily
nonzero
entries
or
one
where
the
0
entries
are
not
in
a
predictable
pattern.The
matrix
associated
with
the
system
can
be
placed
in
secondary
storage
in
partitioned
form
and
portions
read
into
main
memory
only
as
needed
for
calculation.Methods
that
require
secondary
storage
can
be
either
iterative
or
direct,but
they
generally
require
techniques
from
the
fields
of
data
structures
and
graph
theory.The
reader
is
referred
to(BuR)and(RW)for
a
discussion
of
the
current
techniques.
The
software
for
matrix
operations
and
the
direct
solution
of
linear
systems
implemented
in
IMSL
and
NAG
is
based
on
LAPACK,a
subroutine
package
in
the
public
domain.There
is
excellent
documentation
available
with
it
and
from
the
books
written
about
it.We
will
focus
on
several
of
the
subroutines
that
are
available
in
all
three
sources.
Accompanying
LAPACK
is
a
set
of
lower-level
operations
called
Basic
Linear
Algebra
Subprograms(BLAS).Level
1
of
BLAS
generally
consists
of
vector-vector
operations
with
input
data
and
operation
counts
of
O(n).Level
2
consists
of
the
matrix-vector
operations
with
input
data
and
operation
counts
of
O(n2).Level
3
consists
of
the
matrix-matrix
operations
with
input
data
and
operation
counts
of
O(n3).For
example,in
Level
1,the
subroutine
SCOPY
overwrites
a
vector
y
with
a
vector
x;
SSCAL
computes
a
scalar
a
times
a
vector
x;
SAXPY
adds
a
scalar
a
times
a
vector
x
to
a
vector
y(y
=
a•x+y);
SDOT
computes
the
inner,or
scalar,product
of
two
vectors;
SNRM2
computes
the
Euclidean
norm
of
a
vector
by
a
method
similar
to
that
discussed
in
Section
1.4;
and
ISAMAX
computes
the
index
of
the
vector
component
that
gives
the
maximum
absolute
value
of
all
the
components.In
Level
2,SGEMV
computes
the
product
of
a
matrix
and
a
vector
and
in
Level
3,SGEMM
computes
the
product
of
a
matrix
and
a
matrix.

编辑推荐

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图书封面

图书标签Tags

数学,数值计算,numerical_analysis,计算机,英文原版,数值分析,计算机科学


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用户评论 (总计8条)

 
 

  •     一本很好的学习数值分析的书
  •     也可用作社会学专业英语的参考书,还是可以以看看的
  •     看这个好艰难,就是书被折了。
  •     很不错。,送货慢了点。
  •     今夏,听说还不错!
  •     什么都不说了,一本好书
  •     不过还是建议有兴趣的同学们去看原版的montecarlo,买来还没看
  •     但书的质量很好,
 

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