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 r ...

or nonlinear equations. MINPACK, along with other similar libraries such as LINPACK and

EISPACK EISPACK is a software library for numerical computation of eigenvalues and eigenvectors of matrices, written in FORTRAN. It contains subroutines for calculating the eigenvalues of nine classes of matrices: complex general, complex Hermitian, real ...

, originated from the Mathematics and Computer Science Division Software (MCS) of

Argonne National Laboratory Argonne National Laboratory is a science and engineering research United States Department of Energy National Labs, national laboratory operated by University of Chicago, UChicago Argonne LLC for the United States Department of Energy. The facil ...

. Written by Jorge Moré,

Burt Garbow Burt is a given name and also a shortened form of other names, such as Burton and Herbert, or a place name. Burt may refer to: People *Burt Alvord (1866–after 1910), American Old West lawman and outlaw *Burt Bacharach (born 1928), American com ...

, and

Ken Hillstrom Ken or KEN may refer to: Entertainment * ''Ken'' (album), a 2017 album by Canadian indie rock band Destroyer. * ''Ken'' (film), 1964 Japanese film. * ''Ken'' (magazine), a large-format political magazine. * Ken Masters, a main character in ...

, 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 sq ...

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 as ...

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. {{reflist

External links

Netlib download site

User 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