I want to plot region for z numbers that satisfy D<10^-4.

Question

Leia 2022-6-8

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1736705-i-want-to-plot-region-for-z-numbers-that-satisfy-d-10-4

评论： Torsten 2022-6-10

How do I plot the region showing z=x+iy values that make the difference between a polynomial and an exponential function less than 10^-4?

For example;

syms z
[x,y]=meshgrid(-6:.1:2,-6:.1:6);
z=x+1i*y;
R = - 0.0000000000000042786173933199698996786792332228*z.^16 + 0.000000000000093679201874795131075154866430805*z.^15 ...
    - 0.0000000000018102462775238750488561630646573*z.^14 + 0.000000000070607888835529581094992975687635*z.^13 ...
    - 0.00000000047430380749604348847250198255397*z.^12 + 0.0000000060302178555555310479780219749732*z.^11 ...
    - 0.00000014850754796722791834393401507891*z.^10 - 0.0000011975088237244406931082370289037*z.^9 ...
    - 0.00000486020688657407415163842024264*z.^8 + 0.000027465820312500018146735337769556*z.^7 ...
    + 0.0010023328993055556912781216101668*z.^6 + 0.0080891927083333337897961540664676*z.^5 ...
    + 0.041666666666666667576168711195926*z.^4 + 0.16666666666666666756898545265065*z.^3 + 0.5*z.^2 + 1.0*z + 1.0;
T = exp(z);
D = R-T;

I want to plot region for z numbers that satisfy D<10^-4.

How can I do that? I would be appreciate if you help.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Torsten 2022-6-8

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1736705-i-want-to-plot-region-for-z-numbers-that-satisfy-d-10-4#answer_981860

编辑：Torsten 2022-6-8

在 MATLAB Online 中打开

R1 = @(x,y)- 0.0000000000000042786173933199698996786792332228*(x+1i*y).^16 + 0.000000000000093679201874795131075154866430805*(x+1i*y).^15 ...

- 0.0000000000018102462775238750488561630646573*(x+1i*y).^14 + 0.000000000070607888835529581094992975687635*(x+1i*y).^13 ...

- 0.00000000047430380749604348847250198255397*(x+1i*y).^12 + 0.0000000060302178555555310479780219749732*(x+1i*y).^11 ...

- 0.00000014850754796722791834393401507891*(x+1i*y).^10 - 0.0000011975088237244406931082370289037*(x+1i*y).^9 ...

- 0.00000486020688657407415163842024264*(x+1i*y).^8 + 0.000027465820312500018146735337769556*(x+1i*y).^7 ...

+ 0.0010023328993055556912781216101668*(x+1i*y).^6 + 0.0080891927083333337897961540664676*(x+1i*y).^5 ...

+ 0.041666666666666667576168711195926*(x+1i*y).^4 + 0.16666666666666666756898545265065*(x+1i*y).^3 + 0.5*(x+1i*y).^2 + 1.0*(x+1i*y) + 1.0;

R2 = @(x,y) sum((x+1i*y).^(0:16)./factorial(0:16));

T = @(x,y) exp(x+1i*y);

fun1 = @(x,y)norm(R1(x,y)-T(x,y))-1e-4;

fun2 = @(x,y)norm(R2(x,y)-T(x,y))-1e-4;

fimplicit(fun1)

Warning: Function behaves unexpectedly on array inputs. To improve performance, properly vectorize your function to return an output with the same size and shape as the input arguments.

hold on

fimplicit(fun2)

Warning: Function behaves unexpectedly on array inputs. To improve performance, properly vectorize your function to return an output with the same size and shape as the input arguments.