Specialization for banded Jacobians

[ivan-pi]

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Many computational problems will have banded matrices. In those cases a performance increase can be expected from using specialized routines for banded storage.

This question appeared previously on scicomp.stackexchange: https://scicomp.stackexchange.com/questions/36703/nonlinear-root-solving-libraries-which-accept-a-jacobian-in-band-storage

MINPACK uses a QR factorization for the Jacobians. Unfortunately, LAPACK does not provide QR routines for banded Jacobians, however a library does exist for this purpose:

• LAPACK-Style Codes for the QR Factorization of Banded Matrices
• BAND_QR (contains sources for the routines of Remon et al.)

A similar specialization could be pursued for sparse matrices.