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Kung-Traub (J ACM 21:643-651, 1974) constructed two optimal general iterative methods without memory for finding solution of nonlinear equations. In this work, we are going to show that one of them can be applied for matrix inversion. It is observed that the convergence order 2 m can be attained using 2m matrix-matrix multiplications. Moreover, a method with the efficiency index 10 1/6 ≈ 1.4677 will be furnished. To justify that our procedure works efficiently, some numerical problems are included.

In this work, we propose a new fourth-order Jarratt-type method for solving systems of nonlinear equations. The local convergence order of the method is proven analytically. Finally, we validate our results via some numerical experiments including an application to the Chandrashekar integral equations.

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