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- Can PARDISO routines exploit an initial guess?

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greiner08

Beginner

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10-28-2018
07:53 AM

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Can PARDISO routines exploit an initial guess?

I'm using PARDISO to find vector x in the equation

Ax = b

Where A is a real unsymmetric matrix. In the PARDISO manual, they mention the vector x is only accessed in the solution phase.

If I initially have a pretty good estimate of what X is, can I use that estimate somehow (like I can in, say, the Jacobi or Gauss-Seidel algorithm)?

Thanks

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mecej4

Black Belt

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10-29-2018
04:55 AM

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The 'D' in PARDISO stands for "direct". We can roughly think of the algorithm used in Pardiso as a sophisticated version of Gaussian Elimination that is sparseness-aware. Thus, it is a direct method, not an iterative method. There is a provision for iterative refinement, whose purpose is to improve the last few bits in the solution.

Typically, iteration is used to solve a nonlinear problem by solving a sequence of linear problems.

I do not understand your motivation in seeking to use a trial solution for an already linear problem, but you can experiment as follows to clarify matters for yourself. Suppose you have a trial solution x_{0} for A x = b. Calculate b_{1} = b - A x_{0}, exploiting the sparsity of A in computing the matrix-vector product. Now solve A δ = b_{1}, using Pardiso. If the norm of δ is not negligible compared to the norm of x_{0}, the initial guess was no good, and we have wasted some CPU time just to establish that.

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For more complete information about compiler optimizations, see our Optimization Notice.