MINPACK is a library of
FORTRAN subroutines for the solving of
systems of nonlinear equations, or the
least-squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...
minimization of the residual of a set of
linear
Linearity is the property of a mathematical relationship ('' function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear ...
or nonlinear equations.
MINPACK, along with other similar libraries such as
LINPACK and
EISPACK, originated from the Mathematics and Computer Science Division Software (MCS) of
Argonne National Laboratory
Argonne National Laboratory is a science and engineering research national laboratory operated by UChicago Argonne LLC for the United States Department of Energy. The facility is located in Lemont, Illinois, outside of Chicago, and is the lar ...
. Written by
Jorge Moré,
Burt Garbow, and
Ken Hillstrom, MINPACK is free and designed to be highly
portable
Portable may refer to:
General
* Portable building, a manufactured structure that is built off site and moved in upon completion of site and utility work
* Portable classroom, a temporary building installed on the grounds of a school to provide a ...
, robust and reliable. The quality of its implementation of the
Levenberg–Marquardt algorithm
In mathematics and computing, the Levenberg–Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least s ...
is attested by Dennis and Schnabel.
Five algorithmic paths each include a core subroutine and a driver routine. The algorithms proceed either from an analytic specification of the
Jacobian matrix
In vector calculus, the Jacobian matrix (, ) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. When this matrix is square, that is, when the function takes the same number of variables ...
or directly from the problem functions. The paths include facilities for systems of equations with a
banded Jacobian matrix, for least-squares problems with a large amount of data, and for checking the consistency of the Jacobian matrix with the functions.
References
* J. J. Moré, B. S. Garbow, and K. E. Hillstrom
User Guide for MINPACK-1 Argonne National Laboratory Report ANL-80-74, Argonne, Ill., 1980.
* J. J. Moré, D. C. Sorensen, K. E. Hillstrom, and B. S. Garbow, The MINPACK Project, in Sources and Development of Mathematical Software, W. J. Cowell, ed., Prentice-Hall, pages 88–111, 1984.
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External links
Netlib download siteUser Guide for MINPACK-1, Chapters 1 to 3 from J. J. Moré website
User Guide for MINPACK-1, Chapter 4 from J. J. Moré website
Fortran libraries
Numerical software