Roanoke Times
                 Copyright (c) 1995, Landmark Communications, Inc.

DATE: TUESDAY, August 23, 1994                   TAG: 9408270016
SECTION: WELCOME STUDENTS                    PAGE: 55   EDITION: NEW RIVER VALLEY 
SOURCE: New River Valley bureau
DATELINE: RADFORD                                 LENGTH: Medium

RU PROF SPEEDS UP THE ANSWER

An engineer had to calculate how much that bridge you drive across could tolerate before it collapses. Someone had to decide how many beams to install in your home's ceiling so the roof wouldn't fall. Undoubtedly, the calculations used to figure out such everyday breaking points involve Newton's Method in one form or another.

The method, sometimes known as the Newton-Raphson Method, has been around for the better part of 300 years. Today it has undergone another improvement.

Radford University mathematics professor Juergen Gerlach has added a refinement. His paper, "Accelerated Convergence in Newton's Method," was published in the latest issue of the SIAM Review, the quarterly publication of the Society for Industrial and Applied Mathematics.

"I came up with it accidentally," Gerlach said in a Radford University news release. "I was working on some optimization problem, reviewing my math, doing it carefully and then - all of a sudden - I had an idea."

In his paper, Gerlach, a member of Radford's faculty since 1987, shows a way to obtain answers more quickly when using Newton's Method. This allows mathematicians, engineers or physicists to use Newton's Method more efficiently.

"When you run into an equation, eventually you'll need a numerical value of the solution. That's where Newton's Method comes into play," Gerlach said.

Many methods are used to solve such problems as bridge stress and other equations. Bi-section, the secant method, and other iteration methods are being used, but they're not always pragmatic, Gerlach said. "There's no telling how long it will take.

"With my method, any speed of convergence can be achieved, but you'll have to use derivatives," he said. "To converge faster, you must use higher-order derivatives. But that's the price you have to pay. There's no free lunch."