topic Solution to the system of linear equations (Ax=b) with a tridiagonal matrix A in Intel® oneAPI Math Kernel Library & Intel® Math Kernel Library
https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/Solution-to-the-system-of-linear-equations-Ax-b-with-a/m-p/1163816#M28078
<P><SPAN style="font-size: 1em;">Dear all,</SPAN></P>
<P>I'm using ZGTSV routine in order to solve a system of linear equations (Ax=b), where A is a tridiagonal matrix which may not be diagonally dominant (depends on initial values). For a while now I have detected some errors regarding the method used in the ?GTSV routines. Specially I have found that Gauss elimination loses precision due to accumulated round-off errors. I believe that this is my case since the amplitude of the errors increases from x(N) to x(1) (maybe due to backsubstitution?). To test this I actually placed in the x array the data backwards x(N:1) and made the necessary changes to the A matrix and vector b. <BR />
<BR />
Now I was thinking of using iterative methods (Jacobi or Gauss-Seidel) instead of direct method (Gauss elimination) but I couldn't find any routine that would do this for me. Is there one?<BR />
<BR />
BTW: does anyone know any better method to solve my problem?<BR />
<BR />
Thank you in advance for your help</P>
<P>Best regards<BR />
Josué Lopes</P>
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<P> </P>
<P> </P>
<P> </P>Mon, 27 Nov 2017 20:11:19 GMTJosue_L_2017-11-27T20:11:19ZSolution to the system of linear equations (Ax=b) with a tridiagonal matrix A
https://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/Solution-to-the-system-of-linear-equations-Ax-b-with-a/m-p/1163816#M28078
<P><SPAN style="font-size: 1em;">Dear all,</SPAN></P>
<P>I'm using ZGTSV routine in order to solve a system of linear equations (Ax=b), where A is a tridiagonal matrix which may not be diagonally dominant (depends on initial values). For a while now I have detected some errors regarding the method used in the ?GTSV routines. Specially I have found that Gauss elimination loses precision due to accumulated round-off errors. I believe that this is my case since the amplitude of the errors increases from x(N) to x(1) (maybe due to backsubstitution?). To test this I actually placed in the x array the data backwards x(N:1) and made the necessary changes to the A matrix and vector b. <BR />
<BR />
Now I was thinking of using iterative methods (Jacobi or Gauss-Seidel) instead of direct method (Gauss elimination) but I couldn't find any routine that would do this for me. Is there one?<BR />
<BR />
BTW: does anyone know any better method to solve my problem?<BR />
<BR />
Thank you in advance for your help</P>
<P>Best regards<BR />
Josué Lopes</P>
<P> </P>
<P> </P>
<P> </P>
<P> </P>
<P> </P>Mon, 27 Nov 2017 20:11:19 GMThttps://community.intel.com/t5/Intel-oneAPI-Math-Kernel-Library/Solution-to-the-system-of-linear-equations-Ax-b-with-a/m-p/1163816#M28078Josue_L_2017-11-27T20:11:19Z