- 1、本文档共45页,可阅读全部内容。
- 2、有哪些信誉好的足球投注网站(book118)网站文档一经付费(服务费),不意味着购买了该文档的版权,仅供个人/单位学习、研究之用,不得用于商业用途,未经授权,严禁复制、发行、汇编、翻译或者网络传播等,侵权必究。
- 3、本站所有内容均由合作方或网友上传,本站不对文档的完整性、权威性及其观点立场正确性做任何保证或承诺!文档内容仅供研究参考,付费前请自行鉴别。如您付费,意味着您自己接受本站规则且自行承担风险,本站不退款、不进行额外附加服务;查看《如何避免下载的几个坑》。如果您已付费下载过本站文档,您可以点击 这里二次下载。
- 4、如文档侵犯商业秘密、侵犯著作权、侵犯人身权等,请点击“版权申诉”(推荐),也可以打举报电话:400-050-0827(电话支持时间:9:00-18:30)。
查看更多
PADE APPROXIMATION BY RATIONAL FUNCTION 129
We can apply this formula to get the polynomial approximation directly for
a given function f (x), without having to resort to the Lagrange or Newton
polynomial. Given a function, the degree of the approximate polynomial, and the
left/right boundary points of the interval, the above MATLAB routine “cheby()”
uses this formula to make the Chebyshev polynomial approximation.
The following example illustrates that this formula gives the same approximate
polynomial function as could be obtained by applying the Newton polynomial
with the Chebyshev nodes.
Example 3.1. Approximation by Chebyshev Polynomial. Consider the problem
of finding the second-degree (N = 2) polynomial to approximate the function
. We make the following program “do_cheby.m”, which uses
the MATLAB routine “cheby()” for this job and uses Lagrange/Newton polynomial
with the Chebyshev nodes to do the same job. Readers can run this program
to check if the results are the same.
3.4 PADE APPROXIMATION BY RATIONAL FUNCTION
Pade approximation tries to approximate a function f (x) around a point xo by a
rational function
(3.4.1)
where are known.
How do we find such a rational function? We write the Taylor series expansion
of f (x) up to degree M + N at x = xo as
130 INTERPOLATION AND CURVE FITTING
Assuming =0for simplicity, we get the coefficients of
such that
(3.4.3)
by solving the following equations:
(3.4.4a)(3.4.4b)
Here, we must first solve Eq. (3.4.4b) for and then substitute di’s
into Eq. (3.4.4a) to obtain
The MATLAB routine “padeap()” implements this scheme to find the coefficient
vectors of the numerator/denominator polynomial of the
Pade approximation for a given function f (x). Note the following things:
? The derivatives up to order (M + N) are
computed numerically by using the routine “difapx()”, that will be introduced
in Section 5.3.
? In order to compute the values of the Pade approximate function, we substitute
for x in which has been obtaine
您可能关注的文档
- 2013-2014学年沪教牛津版八年级英语下期末检测题及答案.docx
- 西方经济学复习重点无敌版(含图).doc
- 2013-北京市房屋租赁合同(国土资源和房屋管理局-工商局).pdf
- 《乱世》游戏策划书.doc
- 《论美国的民主》读后感.doc
- 2013电子科大研究生图论考试-附答案.pdf
- 西南交大桥梁基础工程课程设计2号墩2003.doc
- 电涡流位移传感器设计.doc
- 《旅游企业经营管理》教学大纲.doc
- 《民法总则》各章重点条文解读.docx
- 中国国家标准 GB/T 18233.4-2024信息技术 用户建筑群通用布缆 第4部分:住宅.pdf
- GB/T 18233.4-2024信息技术 用户建筑群通用布缆 第4部分:住宅.pdf
- GB/T 18978.210-2024人-系统交互工效学 第210部分:以人为中心的交互系统设计.pdf
- 《GB/T 18978.210-2024人-系统交互工效学 第210部分:以人为中心的交互系统设计》.pdf
- 中国国家标准 GB/T 18978.210-2024人-系统交互工效学 第210部分:以人为中心的交互系统设计.pdf
- GB/T 16649.2-2024识别卡 集成电路卡 第2部分:带触点的卡 触点的尺寸和位置.pdf
- 《GB/T 16649.2-2024识别卡 集成电路卡 第2部分:带触点的卡 触点的尺寸和位置》.pdf
- 中国国家标准 GB/T 16649.2-2024识别卡 集成电路卡 第2部分:带触点的卡 触点的尺寸和位置.pdf
- GB/T 17889.4-2024梯子 第4部分:铰链梯.pdf
- 《GB/T 17889.4-2024梯子 第4部分:铰链梯》.pdf
文档评论(0)