linsolve behaviour for SYM true and POSDEF false

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Sylvan Elhay 2024-9-29，8:38

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https://ww2.mathworks.cn/matlabcentral/answers/2156175-linsolve-behaviour-for-sym-true-and-posdef-false

评论： Sylvan Elhay 2024-9-30，12:20

Does linsolve use an LDL factoring if the options are SYM true and POSDEF false?

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Torsten 2024-9-29，12:38

编辑：Torsten 2024-9-29，13:12

Your contribution

Thorsten answered my question. RTFM, I guess. Thanks

was not an answer, but just a comment (like your contribution now:

What does "Moved: John D'Errico" mean, please? I'm a newbie to this forum.

)

So @ John D'Errico and me changed the classification from "answer" to "comment".

Concerning your question again:

I read

Description

X = linsolve(A,B) solves the linear system AX = B using one of these methods:

When A is square, linsolve uses LU factorization with partial pivoting.
For all other cases, linsolve uses QR factorization with column pivoting.

linsolve warns if A is ill conditioned (for square matrices) or rank deficient (for rectangular matrices).

But then I saw that you can additionally use an "opts" structure in which you describe special properties of the matrix. So I'm no longer sure if using the "opts" structure makes linsolve switch to more specialized algorithms not mentionned in detail (like chol, e.g., for Hermitian positive definite matrices A).

Following the flowchart under

https://uk.mathworks.com/help/matlab/ref/double.mldivide.html

it seems that for symmetric indefinite matrices LU is used.

Torsten 2024-9-30，10:04

编辑：Torsten 2024-9-30，10:19

linsolve will use the same solver as mldivide if you specify that your matrix is symmetric indefinite, and according to the flowchart of solvers under

https://uk.mathworks.com/help/matlab/ref/double.mldivide.html

mldivide would use LU for full matrices and LDL for sparse matrices. But better you recheck the yes/no cases in the two flowcharts in the "Algorithms" section.

To be sure you could also contact MATLAB support directly:

https://uk.mathworks.com/help/matlab/matlab_env/contact-technical-support.html

Sylvan Elhay 2024-9-30，12:20

Thanks for all the comments.

Background: I am comparing computation times for solution of 2 sparse systems: one is SYM, INDEF and invertible and the other is square and invertible. I am now comparing the times of LU and LDL so there is no checking of matrix structure by Matlab before solving and the timings reflect only the solution process times.

Thanks again.

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Answer 1

Vandit 2024-9-29，8:57

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2156175-linsolve-behaviour-for-sym-true-and-posdef-false#answer_1524195

编辑：Vandit 2024-9-29，9:01

Hello Sylvan,

The "linsolve" function does not use LDL factorization if the options are set to 'SYM' true and 'POSDEF' false. Instead, it will use the appropriate solver based on the properties specified in the options structure. If 'SYM' is true, it will typically use a method suitable for symmetric matrices, but without the positive definiteness condition, it won't specifically apply LDL factorization.

For more information on "linsolve" function, please refer to the below documentation:

https://www.mathworks.com/help/matlab/ref/linsolve.html

Hope this helps.