Moore test using Gray code

The Moore test is a powerful tool for finding all solutions of nonlinear equations. However, this algorithm requires tremendously many interval computations and iterative bisections of regions. This paper describes that Gray code is an effective code for the Moore test. Using the property of the MSB (most significant bit) first algorithm of the Gray code arithmetic, we can perform the Moore test with the least required accuracy, i.e., the least computational cost. Further, we point out that the region bisection corresponds to the MSB first computation by the Gray code arithmetic. Using this fact, we show that the computational results before the bisection are reused for the bisected regions and that the computational cost is considerably reduced.