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I have come across a curious issue when attempting to find the nullspace of a sparse structurally symmetric matrix * A* with PARDISO, i.e. solving the problem

*where b is the zero vector. When I set the RHS (the vector*

**A x = b***) to be identically zero, I get only the trivial solution (*

**b****= the zero vector) with a residual of**

*x**nan*. However, when I make

*arbitrarily small (e.g. all elements = 1e-16) I obtain a solution, but the residual is exceedingly high (on the order of 1, while the elements in the solution vector are on the order of 10^4).*

**b**Am I misusing PARDISO or are we intended to set ** b **to some arbitrarily small value rather than zero when we wish to find the nullspace? Is there sample code that where the goal is to compute the nullspace specifically? I didn't encounter such problems when

**was a vector of ones. If PARDISO cannot compute the nullspace, is there another MKL function which allows for computation of the nullspace of large, real-valued, indefinite, structurally symmetric**

*b***sparse**matrices?

Thank you.

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Hi,

In case of degenerate matrix pardiso find only one solution so it cannot be used for finding set of solution. For your problem it is better to use EE functionality (https://software.intel.com/en-us/mkl-developer-reference-c-extended-eigensolver-routines) - multiply matrix on itself transpose and find zero eigenvectors of resulted matrix

Thanks,

Alex

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