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Preface to the Second Russian Edition
Preface to the First Russian Edition
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accuracy of 0.001 Achilles algebraic equations approximate solution approximate value approximation process approximation x2 arctan arithmetic mean assume the form bucket computation continuous function contraction mapping convergence test cosx cubic equation decrease denote terms containing equa equal equation f(x equation x3 function cp function f(x geometric mean graph Hence initial approximation instance iteration process linear equations mapping cp(x mathematics method of chords method of iterations method of successive methods of approximate metric space Newton's method perimeter plane point A1 point of intersection point with abscissa point x0 polynomial f(x problem process of successive proved put P0 quadratic equation rate of convergence right-hand side root lying root sought satisfied secant seen from Fig sequence of numbers side of equation sinx slope solution of equations solve the equation solving equations straight line subinterval Substituting successive approximations Suppose system of equations tangent tend to zero terval tion tortoise x-axis y-axis