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MAtlab & Maxima

Tuesday, October 20, 2009. 多项式插值一般在2-5次为宜，最多不超过6，7次。也就是说，在节点数很多的时候，最好将它们分组，分段，对每段则分别用低次多项式插值，这样效果比较接近真实。片面的追求高次多项式，将不会得到好结果。一个著名的例子是Runge给的，他是Weierstruss在Berlin的学生，也是F. Klein在Gottingen的同事。用于模拟常微分方程的解的重要的一类迭代法，龙格－库塔法（Runge-Kutta）是由他和Kutta共同发明的。月球上的Runge陨石坑 (Runge crater) 以他命名。在[-1，1]内取n 1（在这里取n=10）个等距节点，做n次牛顿插值的结果如下，. 其中红线为插值结果，黑线为被插值的函数，可以看出，在[-.2，.2]区间内，插值结果很好，但随着区域的扩大，出现了很大的偏差，特别是在-1，1两点附近，插值多项式基本不能描述被插函数。 X node =-1:.2:1;. Y node = 1./(1 25.*x node.*x node);. A = mynewtonCoeff(x node,y node);.

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MAtlab & Maxima | matlabtips.blogspot.com Reviews

<META> DESCRIPTION

Tuesday, October 20, 2009. 多项式插值一般在2-5次为宜，最多不超过6，7次。也就是说，在节点数很多的时候，最好将它们分组，分段，对每段则分别用低次多项式插值，这样效果比较接近真实。片面的追求高次多项式，将不会得到好结果。一个著名的例子是Runge给的，他是Weierstruss在Berlin的学生，也是F. Klein在Gottingen的同事。用于模拟常微分方程的解的重要的一类迭代法，龙格－库塔法（Runge-Kutta）是由他和Kutta共同发明的。月球上的Runge陨石坑 (Runge crater) 以他命名。在[-1，1]内取n 1（在这里取n=10）个等距节点，做n次牛顿插值的结果如下，. 其中红线为插值结果，黑线为被插值的函数，可以看出，在[-.2，.2]区间内，插值结果很好，但随着区域的扩大，出现了很大的偏差，特别是在-1，1两点附近，插值多项式基本不能描述被插函数。 X node =-1:.2:1;. Y node = 1./(1 25.*x node.*x node);. A = mynewtonCoeff(x node,y node);.

<META> KEYWORDS

1 matlab and maxima

2 runge kutta 现象

3 这就是runge kutta现象

4 源代码如下，

5 demo rungekutta m

6 mynewtoncoeff m

7 mynewtonpoly m

8 posted by howell

9 no comments

10 ax=b直接法

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matlab and maxima,runge kutta 现象,这就是runge kutta现象,源代码如下，,demo rungekutta m,mynewtoncoeff m,mynewtonpoly m,posted by howell,no comments,ax=b直接法,ax=b是数值分析的基础，没有几个算法里面不需要解线性方程组的,loads,解ax=b的法子大概可分为两类，,dolittle's decomposition,returns a= l u,for i =1 n 1,x=b;

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MAtlab & Maxima | matlabtips.blogspot.com Reviews

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Tuesday, October 20, 2009. 多项式插值一般在2-5次为宜，最多不超过6，7次。也就是说，在节点数很多的时候，最好将它们分组，分段，对每段则分别用低次多项式插值，这样效果比较接近真实。片面的追求高次多项式，将不会得到好结果。一个著名的例子是Runge给的，他是Weierstruss在Berlin的学生，也是F. Klein在Gottingen的同事。用于模拟常微分方程的解的重要的一类迭代法，龙格－库塔法（Runge-Kutta）是由他和Kutta共同发明的。月球上的Runge陨石坑 (Runge crater) 以他命名。在[-1，1]内取n 1（在这里取n=10）个等距节点，做n次牛顿插值的结果如下，. 其中红线为插值结果，黑线为被插值的函数，可以看出，在[-.2，.2]区间内，插值结果很好，但随着区域的扩大，出现了很大的偏差，特别是在-1，1两点附近，插值多项式基本不能描述被插函数。 X node =-1:.2:1;. Y node = 1./(1 25.*x node.*x node);. A = mynewtonCoeff(x node,y node);.

INTERNAL PAGES

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MAtlab & Maxima: Runge Kutta 现象

http://matlabtips.blogspot.com/2009/10/runge-kutta.html

Tuesday, October 20, 2009. 多项式插值一般在2-5次为宜，最多不超过6，7次。也就是说，在节点数很多的时候，最好将它们分组，分段，对每段则分别用低次多项式插值，这样效果比较接近真实。片面的追求高次多项式，将不会得到好结果。一个著名的例子是Runge给的，他是Weierstruss在Berlin的学生，也是F. Klein在Gottingen的同事。用于模拟常微分方程的解的重要的一类迭代法，龙格－库塔法（Runge-Kutta）是由他和Kutta共同发明的。月球上的Runge陨石坑 (Runge crater) 以他命名。在[-1，1]内取n 1（在这里取n=10）个等距节点，做n次牛顿插值的结果如下，. 其中红线为插值结果，黑线为被插值的函数，可以看出，在[-.2，.2]区间内，插值结果很好，但随着区域的扩大，出现了很大的偏差，特别是在-1，1两点附近，插值多项式基本不能描述被插函数。 X node =-1:.2:1;. Y node = 1./(1 25.*x node.*x node);. A = mynewtonCoeff(x node,y node);.

2

MAtlab & Maxima: Ax=b直接法

http://matlabtips.blogspot.com/2009/10/axb.html

Sunday, October 11, 2009. Linear, algebraic equations occur in almost all branches of numerical analysis. But their most visible application in engineering is in the analysis of linear systems (any. System whose response is proportional to the input is deemed to be linear). Linear systems include structures, elastic solids, heat flow, seepage of fluids, electromagnetic fields and electric circuits; i.e.,most topics taught in an engineering curriculum. If the system is discrete, such as a truss（桁架. The c...

3

MAtlab & Maxima: March 2009

http://matlabtips.blogspot.com/2009_03_01_archive.html

Wednesday, March 4, 2009. Today install the symbolic toolbox. Here is a example to plot scalar field with surface and contour. Also the gradient and others. X,Y] = meshgrid(-15:.5:15, -10:.5:10);. Z = 50 * exp(-X. 2/90 - Y. 2/25);. Surface of Z(X,Y). Figure,surf(X,Y,Z),colorbar,axis equal. C,h] = contour(X,Y,Z); clabel(c,h), colorbar,axis equal. Px,py] = gradient(Z,.2,.15);. C,h] = contour(X,Y,Z); colorbar,axis equal,hold on. QUIVER(X,Y,U,V) plots velocity vectors as arrows with components (u,v).

4

MAtlab & Maxima: GNU TeXmacs Tutorial

http://matlabtips.blogspot.com/2009/07/gnu-texmacs-tutorial.html

Monday, July 6, 2009. Http:/ www.texmacs.org/Tutorial/. You may start TeXmacs by typing. The first time that you start TeXmacs, the program will analyze your system in order to test whether all other packages which are needed by TeXmacs are present on your system. If no problems occur, then a. With the following aspect should appear on your screen:. Subscribe to: Post Comments (Atom).

5

MAtlab & Maxima: June 2009

http://matlabtips.blogspot.com/2009_06_01_archive.html

Monday, June 15, 2009. Bitwise operations are operations which occur to the individual bits of a number. For example, 5 is written as 101 in base 2, that is,. In this case, operations occur on the individual bits. For example, bit-wise and 3 and 5 is the and of the corresponding bits. Subscribe to: Posts (Atom).

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MAtlab & Maxima

Tuesday, October 20, 2009. 多项式插值一般在2-5次为宜，最多不超过6，7次。也就是说，在节点数很多的时候，最好将它们分组，分段，对每段则分别用低次多项式插值，这样效果比较接近真实。片面的追求高次多项式，将不会得到好结果。一个著名的例子是Runge给的，他是Weierstruss在Berlin的学生，也是F. Klein在Gottingen的同事。用于模拟常微分方程的解的重要的一类迭代法，龙格－库塔法（Runge-Kutta）是由他和Kutta共同发明的。月球上的Runge陨石坑 (Runge crater) 以他命名。在[-1，1]内取n 1（在这里取n=10）个等距节点，做n次牛顿插值的结果如下，. 其中红线为插值结果，黑线为被插值的函数，可以看出，在[-.2，.2]区间内，插值结果很好，但随着区域的扩大，出现了很大的偏差，特别是在-1，1两点附近，插值多项式基本不能描述被插函数。 X node =-1:.2:1;. Y node = 1./(1 25.*x node.*x node);. A = mynewtonCoeff(x node,y node);.

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