NEWTON_RC
Newton Method with Reverse Communication

NEWTON_RC is a FORTRAN77 program which is a simple demonstration of solving a system of nonlinear equations with Newton's method, using reverse communication (RC).

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

NEWTON_RC is available in a FORTRAN77 version.

Related Data and Programs:

BACKTRACK_BINARY_RC, a FORTRAN77 library which carries out a backtrack search for a set of binary decisions, using reverse communication (RC).

BISECTION_RC, a FORTRAN77 library which seeks a solution to the equation F(X)=0 using bisection within a user-supplied change of sign interval [A,B]. The procedure is written using reverse communication (RC).

CG_RC, a FORTRAN77 library which implements the conjugate gradient method for solving a positive definite sparse linear system A*x=b, using reverse communication (RC).

KELLEY, a MATLAB library which can seek solutions of systems of nonlinear equations.

MINPACK, a FORTRAN90 library which is a minimization package for which most of these problems were used as tests, as part of ACM TOMS algorithm 566.

SORT_RC, a FORTRAN77library which can sort a list of any kind of objects, using reverse communication (RC).

ZERO_RC, a FORTRAN77 library which seeks solutions of a scalar nonlinear equation f(x) = 0, or a system of nonlinear equations, using reverse communication (RC).

Reference:

1. James Ortega, Werner Rheinboldt
   Iterative Solution of Nonlinear Equations in Several Variables,
   SIAM, 1987,
   ISBN13: 978-0898714616,
   LC: QA297.8.O77.
2. Werner Rheinboldt,
   Methods for Solving Systems of Nonlinear Equations,
   SIAM, 1998,
   ISBN: 089871415X,
   LC: QA214.R44.

Source Code:

• newton_rc.f, the source code.
• newton_rc.sh, commands to compile the source code.

Examples and Tests:

• newton_rc_prb.f, a sample calling program.
• newton_rc_prb.sh, commands to compile and run the sample program.
• newton_rc_prb_output.txt, the output file.

List of Routines:

• NEWTON_RC solves a small system of nonlinear equations.
• R8_EPSILON returns the R8 roundoff unit.
• DAXPY computes constant times a vector plus a vector.
• DDOT forms the dot product of two vectors.
• DGEFA factors a double precision matrix by gaussian elimination.
• DGESL solves a linear system factored by DGEFA.
• DSCAL scales a vector by a constant.
• DSWAP interchanges two vectors.
• IDAMAX finds the index of element having maximum absolute value.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.