An Approximate Solver for Symbolic Equations

This paper describes a program, called NEWTON, that finds approximate symbolic solutions to parameterized equations in one variable. N E W T O N derives an initial approximation by solving for the dominant term in the equation, or if this fails, by bisection. It refines this approximation by a symbolic version of Newton's method. It tests whether the first Newton iterate lies closer to the solution than does the initial solution. If so, it returns this iterate; otherwise, it chooses a new initial solution and tries again. 1 I n t r o d u c t i o n Research in symbolic equation solving has focused on exact solution methods. The resulting programs, such as MACSYMA [Mathlab Group, 1983] and PRESS [Bundy and Welham, 198l], either return an exact solution or fail. Yet, scientists and engineers routinely must solve problems that have no exact closed-form solution. They need an equation solver that finds adequate approximate solutions to such problems, rather than failing. In fact, they...

• Type: Conference
• Year: 1989
• Where: IJCAI
• Authors: Elisha Sacks
• Keywords: Exact Solution, IJCAI 1989, IJCAI 2007, Parameterized Equations, Solutions