Solving system of equations

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BeeTiaw 2018-1-1

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评论： Jan 2019-4-25

采纳的回答： Matt J

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Hi expert,

May I ask your suggestion on how to solve the following matrix system,

where the component of the matrix A is complex numbers with the angle (theta) runs from 0 to 2*pi, and n = 9. The known value z = x + iy = re^ia, is also complex numbers as such, r = sqrt(x^2+y^2) and a = atan (y/x)

Suppose matrix z is as shown below,

z =

         0    1.0148
1736    0.9848
3420    0.9397
5047    0.8742
6748    0.8042
8419    0.7065
9919    0.5727
1049    0.4022
1757    0.2073
1999         0
1757   -0.2073
1049   -0.4022
9919   -0.5727
8419   -0.7065
6748   -0.8042
5047   -0.8742
3420   -0.9397
1736   -0.9848
         0   -1.0148

How do you solve the system of equations above i.e. to find the coefficient of matrix alpha. I tried using a simple matrix manipulation X = inv((tran(A)*A))*tran(A)*z, but I cannot get a reasonable result.

I would expect the solution i.e. components of matrix alpa to be a real numbers.

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采纳的回答

Matt J 2018-1-1

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https://ww2.mathworks.cn/matlabcentral/answers/375136-solving-system-of-equations#answer_298280

编辑：Matt J 2018-1-1

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What do the two columns of z mean? Is the 2nd column supposed to be the imaginary part of z? If so,

Z=complex(z(:,1),z(:,2));
X = A\Z

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BeeTiaw 2018-2-16

编辑：BeeTiaw 2018-2-16

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Hi MattJ,

Thanks for your prompt response.

Because the first component must equal to 1, then I would expect the problem can only be solved iteratively? Isn't it?

Unless you know how to solve them analytically, I would be happy to use the method.

Below is the system that I want to solve (slightly modified from the original post)

Where the angle (theta) runs from 0 to 2*pi which has m divisions, and n = 9.

Notice that the value of the first component of the desired constants must equal 1.

The known value z = x + iy = re^ia, is also complex numbers as such, r = sqrt(x^2+y^2) and a = atan (y/x)

Suppose matrix z is as shown below,

z =
           0    1.0148
1736    0.9848
3420    0.9397
5047    0.8742
6748    0.8042
8419    0.7065
9919    0.5727
1049    0.4022
1757    0.2073
1999         0
1757   -0.2073
1049   -0.4022
9919   -0.5727
8419   -0.7065
6748   -0.8042
5047   -0.8742
3420   -0.9397
1736   -0.9848
           0   -1.0148

Matt J 2018-2-17

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If the first value is 1, then this just leads to a mild modification of my initial proposal,

zc=complex(z(:,1),z(:,2));
alpha=A(:,2:end)\(zc-A(:,1))

This solves for the unknown alpha (alpha2,...,alphaN).

Jan 2019-4-25

@BeeTiaw: Which code do you consider as correct? What does "it seems that I have not got the right answer" mean? Which answer from which code to which input is meant here?

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