On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations

Table 1

Comparison of efficiency indices for different methods.

Iterative methods	(1.2)	(1.5)	(1.6)	(2.2)
Number of steps	1	2	2	3
Rate of convergence	2	4	4	6
Number of functional evaluations	𝑛+𝑛^2	𝑛+2𝑛^2	𝑛+2𝑛^2	2𝑛+2𝑛^2
The classical efficiency index	2^1/(𝑛+𝑛2)	4^1/(𝑛+2𝑛2)	4^1/(𝑛+2𝑛2)	6^1/(2𝑛+2𝑛2)
Number of LU factorizations	1	2	2	1
Cost of LU factorizations; (based on flops)	2𝑛^3/3	4𝑛^3/3	4𝑛^3/3	2𝑛^3/3
Cost of linear systems (based on flops)	2𝑛^3/3+2𝑛^2	10𝑛^3/3+2𝑛^2	7𝑛^3/3+2𝑛^2	5𝑛^3/3+4𝑛^2
Flops-like efficiency index	2^1/((2𝑛3/3)+3𝑛2+𝑛)	4^1/((10𝑛3/3)+4𝑛2+𝑛)	4^1/((7𝑛3/3)+4𝑛2+𝑛)	6^1/((5𝑛3/3)+6𝑛2+2𝑛)