Multi-Linear regression to find a symmetric matrix












0














I am trying to solve a multiple linear regression problem in the form of



$y = A x$



where $y,A,x in mathbb{C}$ with unknown $A$.



This may be reasonably easy by using the normal equation for regression. However, in my case I would like to find a symmetric complex matrix $A$.



I was think of partitioning the regression into different sub-problems in order to force $A$ to be symmetric. For example, first determine the first row of $A(1,:)$ and then forcing elements $A(:,1) = A(1,:)$. Then continuing with the second row, but only for the upper triangle elements of $A$. This seems not a very elegant solution. Would you have other suggestions how to solve this problem?
Thanks!



Update
I was actually able to solve the problem using convex optimization (cvx Toolbox in Matlab) by solving the following problem:



$text{min} vert A x -y vert_2 $



$text{subject to} forall i ne j quad A_{i,j} = A_{j,i}$



However I was wondering if there is a specific algorithm that would also solve this problem without using the cvx Toolbox?






complex-numbers regression least-squares







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    0














    I am trying to solve a multiple linear regression problem in the form of



    $y = A x$



    where $y,A,x in mathbb{C}$ with unknown $A$.



    This may be reasonably easy by using the normal equation for regression. However, in my case I would like to find a symmetric complex matrix $A$.



    I was think of partitioning the regression into different sub-problems in order to force $A$ to be symmetric. For example, first determine the first row of $A(1,:)$ and then forcing elements $A(:,1) = A(1,:)$. Then continuing with the second row, but only for the upper triangle elements of $A$. This seems not a very elegant solution. Would you have other suggestions how to solve this problem?
    Thanks!



    Update
    I was actually able to solve the problem using convex optimization (cvx Toolbox in Matlab) by solving the following problem:



    $text{min} vert A x -y vert_2 $



    $text{subject to} forall i ne j quad A_{i,j} = A_{j,i}$



    However I was wondering if there is a specific algorithm that would also solve this problem without using the cvx Toolbox?






    complex-numbers regression least-squares







    share|cite|improve this question



























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      1





      I am trying to solve a multiple linear regression problem in the form of



      $y = A x$



      where $y,A,x in mathbb{C}$ with unknown $A$.



      This may be reasonably easy by using the normal equation for regression. However, in my case I would like to find a symmetric complex matrix $A$.



      I was think of partitioning the regression into different sub-problems in order to force $A$ to be symmetric. For example, first determine the first row of $A(1,:)$ and then forcing elements $A(:,1) = A(1,:)$. Then continuing with the second row, but only for the upper triangle elements of $A$. This seems not a very elegant solution. Would you have other suggestions how to solve this problem?
      Thanks!



      Update
      I was actually able to solve the problem using convex optimization (cvx Toolbox in Matlab) by solving the following problem:



      $text{min} vert A x -y vert_2 $



      $text{subject to} forall i ne j quad A_{i,j} = A_{j,i}$



      However I was wondering if there is a specific algorithm that would also solve this problem without using the cvx Toolbox?






      complex-numbers regression least-squares







      share|cite|improve this question















      I am trying to solve a multiple linear regression problem in the form of



      $y = A x$



      where $y,A,x in mathbb{C}$ with unknown $A$.



      This may be reasonably easy by using the normal equation for regression. However, in my case I would like to find a symmetric complex matrix $A$.



      I was think of partitioning the regression into different sub-problems in order to force $A$ to be symmetric. For example, first determine the first row of $A(1,:)$ and then forcing elements $A(:,1) = A(1,:)$. Then continuing with the second row, but only for the upper triangle elements of $A$. This seems not a very elegant solution. Would you have other suggestions how to solve this problem?
      Thanks!



      Update
      I was actually able to solve the problem using convex optimization (cvx Toolbox in Matlab) by solving the following problem:



      $text{min} vert A x -y vert_2 $



      $text{subject to} forall i ne j quad A_{i,j} = A_{j,i}$



      However I was wondering if there is a specific algorithm that would also solve this problem without using the cvx Toolbox?






      complex-numbers regression least-squares




      complex-numbers regression least-squares






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Nov 21 '18 at 17:41

























      asked Nov 21 '18 at 4:42









      Sev N

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