Solution of a non-linear equation

✍ Scribed by W.R. Paterson

• Publisher: Elsevier Science
• Year: 1974
• Tongue: English
• Weight: 74 KB
• Volume: 29
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(74)87021-1

✦ Synopsis

Dear Sirs, W. R. PATERSON In a recent paper, Shacham and Kehat[l] discuss the Department of Chemical Engineering, problem of solving a single non-linear algebraic equation. Unioersity of Edinburgh, They present the following convergence criteria (their King's Buildings, notation and equation numbers)-Mavfield Road. (7) Ediburgh Ek93JL, Scotland fcG+,) x f(Xi) < 0.

(

Thus convergence is deemed to have occurred when two successive iterates are close together and bound the root.

The authors state that criterion ( 15) is not used in the chemical engineering literature. It would appear that they may have overlooked two algorithms which make use of ( 15), namely the Rule of False Position[2] and Cox's method[3], both of which exhibit superlinear convergence[4] and have been successfully applied to chemical engineering problems [5,6].

If the comparison of algorithms had included these two techniques the advantages of the authors' novel algorithms might have been demonstrated more clearly.