Difference between mldivide and lsqr

Question

Jaehoon Jeong 2023-7-21

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1998888-difference-between-mldivide-and-lsqr

编辑： Bruno Luong 2023-7-21

采纳的回答： Bruno Luong

Hi, I am curious about the difference between mldivide and lsqr.

Both seem to be used for calculating x where A*x=b.

Thank you in advance.

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Answer 1

Bruno Luong 2023-7-21

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1998888-difference-between-mldivide-and-lsqr#answer_1276568

编辑：Bruno Luong 2023-7-21

在 MATLAB Online 中打开

The difference manifests obviously when you try to solve underdetermined linear system A*x = b.

A=rand(3,5)
A = 3×5
    0.1391    0.7822    0.5816    0.3031    0.3500
    0.4841    0.6309    0.9509    0.7327    0.0768
    0.7137    0.8771    0.4724    0.4694    0.4100
b=rand(3,1)
b = 3×1
    0.9778
    0.2986
    0.9737

The backslash returns a solution with most 0s and lsqr returns solution with minimum l2-norm.

xbackslash=A\b
xbackslash = 5×1
   -0.4389
    1.8328
   -0.6786
         0
         0
xlsqr=lsqr(A,b)
lsqr converged at iteration 3 to a solution with relative residual 8.3e-14.
xlsqr = 5×1
   -0.1969
    1.1213
   -0.1120
   -0.3746
    0.8767
xminnorm=lsqminnorm(A,b)
xminnorm = 5×1
   -0.1969
    1.1213
   -0.1120
   -0.3746
    0.8767

Both minimize norm(A*x-b,2), in case not overdetermined system A*x match b (as withe example here)

A*xbackslash
ans = 3×1
    0.9778
    0.2986
    0.9737
A*xlsqr
ans = 3×1
    0.9778
    0.2986
    0.9737
norm(xbackslash)
ans = 2.0031
norm(xlsqr) % smaller even xlsqr has no O
ans = 1.4891