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This article proposes to add a simple term to an iterative algebraic equation solver with an order n convergence rate, and to raise the order of convergence to (2n − 1). In particular, a simple algebraic equation solver with the 5 th order convergence but uses only 4 function values in each iteration, is described in details. When this scheme is applied to a Newton-Raphson method of the quadratic convergence for a system of algebraic equations, a cubic convergence can be achieved with an lowdoi:10.2172/1116976 fatcat:nsosunqcebfapndlkzax4yjgya