I have skimmed through the LAPACK user guide, but I could not find if LAPACK offers routines for Krylov Subspace based methods (such as CG or BiCGSTAB etc) and Newton method based nonlinear solvers. Also, are iterative methods available in LAPACK in general?
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2 Answers
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As far as I know, there are no such methods in LAPACK. Since LAPACK is the linear algebra package, no nonlinear solvers are included.
However, you can use the underlying BLAS for implementing iterative methods. For nonlinear solvers using Jacobians (e.g., Newton's method), the matrix factorizations of LAPACK may come in handy.
You may want to have a look at PETSc, though. This library implements many iterative methods (e.g., CG, GMRES, BiCG) and nonlinear solvers (e.g., Quasi-Newton, trust region Newton, Richardson / Picard iteration, Anderson mixing).
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$\begingroup$ Thank you for the response. I actually use PETSc and SLEPc for my research, but I just wanted to confirm if LAPACK has any such implementations. $\endgroup$– pranannaCommented Nov 1, 2020 at 7:56
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LAPACK doesn't include any iterative solvers. The routines in LAPACK are for eigenvalues, matrix factorizations, and solutions of systems of equations involving dense matrices while iterative methods are generally used for matrices that are large and sparse.
answered Nov 1, 2020 at 16:31