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## Pardiso w/ Quasi Newton method?

I have read through the page describing using PARDISO to solve a nonlinear set of equations after they have been linearized, but I noticed the algorithm is just Newton's method applied with the PARDISO solving routing.

For faster and more reliable convergence, has anyone created a Quasi Newton solving algorithm using the PARDISO routine during the external iterations?

J

1 Solution Black Belt
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If the nonlinear equations being solved arise from discretization of nonlinear partial differential equations, application of a quasi-Newton method such as Broyden's scheme would result in a situation where a sparse solver such as Pardiso becomes worthy of consideration. See, for example, http://www.ams.org/journals/mcom/1970-24-109/S0025-5718-1970-0258276-9/ .

Many of the sparse matrices in the NIST Matrix Market collection (http://math.nist.gov/MatrixMarket/index.html) arose from FEA models of stress analysis, flow networks, etc.

3 Replies Employee
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Hi,

I can be wrong, feel free to correct me, but Quasi Newton algorithm construct dense matrix, so it is not a point for Pardiso solver, is not it?

Thanks,

Alex Black Belt
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If the nonlinear equations being solved arise from discretization of nonlinear partial differential equations, application of a quasi-Newton method such as Broyden's scheme would result in a situation where a sparse solver such as Pardiso becomes worthy of consideration. See, for example, http://www.ams.org/journals/mcom/1970-24-109/S0025-5718-1970-0258276-9/ .

Many of the sparse matrices in the NIST Matrix Market collection (http://math.nist.gov/MatrixMarket/index.html) arose from FEA models of stress analysis, flow networks, etc. Beginner
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Alexander and Mecej4

You both are crazy smart, and both spot on. I only know enough to stir up trouble which is why I posted this. PARDISO is, without a doubt, needed to solve A*x = b where A is sparse, hands down no question. I am wanting to eventually update my solver to use a "quasi" Newton's method and was curious if anyone had an implementation posted on these forums or somewhere out there on the webs that utilized PARDISO in this type of iterative algorithm.

Mecej4 thanks for the links those are great resources!

J 