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Algorithm 1 A modified Jacobi matrix on Newton iteration method

From: Effects of HIV infection on CD4+ T-cell population based on a fractional-order model

1: Given \(N_{\mathrm{iter}}\), ε, let Nd = 1
2: if \(k>N_{\mathrm{iter}}\) and \(\|f(x^{k+1})\|>\|f(x^{k})\|\)
3: \(Nd: =\frac{1}{2}Nd\)
4: end if
5: if \(\operatorname{det}(J(x^{k}))<\varepsilon\), %ε is a sufficiently small positive number
6: \(J(x^{k}): =Nd\cdot(J(x^{k})+I)\), %I is an identity matrix
7: else
8: \(J(x^{k}): =Nd\cdot J(x^{k})\)
9: end if
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