unknown user

05-20-1991, 10:47 PM

Dear Biomch-L readers,

Yesterday, Paolo de Leva asked about software

for solving overcomplete systems of nonlinear equations. Overcomplete (or

overdetermined) means that there are more equations than unknowns, and an

exact solution does not exist. Instead, the sum of squares of N nonlinear

functions of M variables is minimized. For this type of problem, I have

has some success with LMDIF, a subroutine from the Netlib library. The

application was least squares fitting of a model to experimental data

(N>>M). LMDIF uses the Levenberg-Marquardt algorithm, which is described

by Levenberg as a generalization of the Newton-Raphson method. For my

application, LMDIF performed much better than SVDMIN. SVDMIN is a routine

from ACCULIB (a local numerical library of our computer center), and is

based on singular value decomposition of the NxM Jacobian matrix.

Both routines are written in Fortran.

LMDIF can be obtained by sending a request to the fileserver netlib@ornl.gov.

Example:

help

send index

send index from minpack

send lmdif1 from minpack

Specify sminpack instead of minpack if you need the single precision version.

Literature (LMDIF):

K. Levenberg (1944) A method for the solution of certain non-linear problems

in least squares. Quart.Appl.Math. 2:164-168.

D.W. Marquardt (1963) An algorithm for least squares estimation of nonlinear

parameters. J.Soc.Industr.Appl.Math. 11:431-441.

(SVDMIN):

J.H. Wilkinson and C. Reinsch (1971) Linear Algebra. Springer Verlag, Berlin.

pp. 134-151. (deals only with the singular value decomposition).

I hope this information is useful for Paolo and others.

-- Ton van den Bogert

Dept. of Veterinary Anatomy

University of Utrecht, Netherlands.

Yesterday, Paolo de Leva asked about software

for solving overcomplete systems of nonlinear equations. Overcomplete (or

overdetermined) means that there are more equations than unknowns, and an

exact solution does not exist. Instead, the sum of squares of N nonlinear

functions of M variables is minimized. For this type of problem, I have

has some success with LMDIF, a subroutine from the Netlib library. The

application was least squares fitting of a model to experimental data

(N>>M). LMDIF uses the Levenberg-Marquardt algorithm, which is described

by Levenberg as a generalization of the Newton-Raphson method. For my

application, LMDIF performed much better than SVDMIN. SVDMIN is a routine

from ACCULIB (a local numerical library of our computer center), and is

based on singular value decomposition of the NxM Jacobian matrix.

Both routines are written in Fortran.

LMDIF can be obtained by sending a request to the fileserver netlib@ornl.gov.

Example:

help

send index

send index from minpack

send lmdif1 from minpack

Specify sminpack instead of minpack if you need the single precision version.

Literature (LMDIF):

K. Levenberg (1944) A method for the solution of certain non-linear problems

in least squares. Quart.Appl.Math. 2:164-168.

D.W. Marquardt (1963) An algorithm for least squares estimation of nonlinear

parameters. J.Soc.Industr.Appl.Math. 11:431-441.

(SVDMIN):

J.H. Wilkinson and C. Reinsch (1971) Linear Algebra. Springer Verlag, Berlin.

pp. 134-151. (deals only with the singular value decomposition).

I hope this information is useful for Paolo and others.

-- Ton van den Bogert

Dept. of Veterinary Anatomy

University of Utrecht, Netherlands.