Multiple-step method for solving nonlinear systems of equations

✍ Scribed by Jsun Yui Wong

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 97 KB
• Volume: 5
• Category: Article
• ISSN: 1061-3773
• DOI: 10.1002/(sici)1099-0542(1997)5:2<121::aid-cae6>3.0.co;2-f

✦ Synopsis

The present method has several steps. The first step starts for each unknown with a random value in the interval for the unknown. The second step starts at a point near the best point obtained in step one; specifically, for each unknown variable, the second step starts with a value which is, say, the first four digits of the value obtained in step one. Going from step two to step three is like going from step one to step two, but more digits, say, the first five digits of the value obtained in step two, are used for step three. Subsequent steps, if needed for higher accuracy than the accuracy already obtained, are similar. For a certain ill-conditioned nonlinear system of nine equations with nine variables, this method yields in step one a solution with a sum of residuals of 8.61rrrD-05 and yields in step four a solution with a sum of residuals of 1.30rrrD-06 and with the worst residual of 3.88rrrD-07.