Algorithm 1 A modified Jacobi matrix on Newton iteration method

1:

Given \(N_{\mathrm{iter}}\), ε, let Nd = 1

2:

if \(k>N_{\mathrm{iter}}\) and \(\|f(x^{k+1})\|>\|f(x^{k})\|\)

3:

  \(Nd: =\frac{1}{2}Nd\)

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end if

5:

if \(\operatorname{det}(J(x^{k}))<\varepsilon\), %ε is a sufficiently small positive number

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  \(J(x^{k}): =Nd\cdot(J(x^{k})+I)\), %I is an identity matrix

7:

else

8:

  \(J(x^{k}): =Nd\cdot J(x^{k})\)

9:

end if