Modified Newton formula of tangent parabolas on the number axis

The paper proposes a modified Newton's formula - tangent parabolas on the real axis. The analytical formula contains a square root (radical) and is applicable for the multiplicity of the root no more than two. It is shown that for a single root the formula with a radical has the third order of the rate of convergence of the residual to zero, while Newton's formula converges with the second order of the rate. For a root multiplicity of two, the order of speed for a formula with a radical is two. The formula with the radical is replaced by a series of eleven terms, that is, it is extended to the numerical axis for any multiplicity of the root. For a root of multiplicity one, an iterative formula of eleven terms is proposed. For the multiplicity of the root two or more, an iterative algorithm with the parameter 0 The paper proposes a modified Newton's formula - tangent parabolas on the real axis. The analytical formula contains a square root (radical) and is applicable for the multiplicity of the root no more than two. It is shown that for a single root the formula with a radical has the third order of the rate of convergence of the residual to zero, while Newton's formula converges with the second order of the rate. For a root multiplicity of two, the order of speed for a formula with a radical is two. The formula with the radical is replaced by a series of eleven terms, that is, it is extended to the numerical axis for any multiplicity of the root. For a root of multiplicity one, an iterative formula of eleven terms is proposed. For the multiplicity of the root two or more, an iterative algorithm with the parameter 0 function show_eabstract() { $('#eabstract1').hide(); $('#eabstract2').show(); $('#eabstract_expand').hide(); } ▼Показать полностью