Computational Science Stack Exchange
Computational Science Stack Exchange

Questions tagged [linear-solver]

Referring to methods for solving linear systems of equations.

Systems of Linear Equations are collections of linear equations involving the same set of variables and can be solved using many different methods.

Questions relating to solution methods for systems of linear equations should be asked here.

Some examples of relevant solution types and question topics are:

  • Elimination of Variables
  • Row Reduction
  • Cramers Rule
  • Matrix methods:matrix decomposition, linear least squares, iterative solutions
  • Using LAPACK or other linear algebra solver libraries
403 questions
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efficiently solving a low rank linear parametric systems?

I have a large number of systems of the form: $Ax=b_i$ To solve for a large numbers of such $b_i\;1\leq i \leq k$ but where $A$ is fixed (A is a rank $p$ general --i.e. non sparse, non PSD-- matrix). I can solve them individually using an LU…
user189035
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What is linsolve() doing?

I'm converting a piece of matlab code to python but I am having difficulty recreating the solution it finds for an overdetermined sparse matrix. The original code used the overloaded left division operator but I have recreated the results using…
jonathanbyrn
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4
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Numeric solution of simple but possibly singular linear system

I have a simple (and small) linear homogeneous system $Ax=0$, where the entries of the $N\times M$ matrix $A$ are small integers. I do not need fancy methods which efficiently solve almost singular matrices and treat roundoff errors etc. But I need…
highsciguy
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How does one proceed to solve (big) underdetermined or overdetermined systems of linear equations "nowadays"?

In my numerical linear algebra class we mentioned this problem briefly and according to some other lectures on the internet especially in data driven environments one mostly has to deal with such over- or underdetermined systems. Nevertheless in our…
Sen90
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Partially Banded Matrix

I have a somewhat peculiar Jx=R system that I need to solve. The matrix J is 2N -by- 2N. The first N rows have all entries filled. The next N rows are banded in two places, i.e. for the (N+k)th row, the (k-1,k,k+1)th and the N+(k-1,k,k+1)th entries…
pkaran
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Iterative solver, which balances the equations with the biggest errors

I am trying to understand the mathematical side of an algorithm, which approximates the solution of coulomb's law. Their approach is to balance the two elements with the biggest positive/negative error. Trying to understand the stability conditions…
allo
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External solver in Abaqus/Ansys

Is it possible to call an external linear solver from Abaqus and/or Ansys? This solver (which is supplied by me) would get the sparse matrix A and the right hand side vector b as inputs, and would return the solution x (with A x = b) to the program.…
Adrian Willenbücher
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Solving a singular system of linear equations with smallest solution?

I have a problem where I am solving a system of linear equations but sometimes the system results in a singular matrix which cannot be easily solved. In this case I would like that those rows for which system is ill-defined would be computed as 0.…
Mitar
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