Method of Successive ApproximationsThe aim of this text is to present several methods for the approximate solution of equations. Most of the methods for the approximate solution of equations are connected with the concept of the derivative, which is introduced with a treatment based on an appeal to geometry. Readers need no background other than high school mathematics. Engineers and other specialists need to solve equations, and familiarity with methods of approximate solution is useful for high school and college students. |
Contents
Preface to the Second Russian Edition | 7 |
Achilles and the Tortoise | 14 |
Extraction of Roots with Positive | 25 |
Copyright | |
5 other sections not shown
Common terms and phrases
a₁ a₁x a₂ abscissa accuracy of 0.001 Achilles an+1 approximate solution approximate value arcsin arctan arithmetic mean b₁ b₂ bucket computation contraction mapping convergence test d₁ decrease denote terms containing derivative distance equa equal equation f(x error f(x₁ formula function f(x geometric mean graph Hence inequality initial approximation x₁ instance iteration process linear equations M₂ mathematics method of chords method of iterations method of successive methods of approximate N₁ Newton's method numbers x1 obtain perimeter point of intersection points x₁ polynomial polynomial f(x problem process of successive proved Putting x₁ rate of convergence region D right-hand side root lying root sought satisfied secant seen from Fig sequence of numbers slope solution of equations solve the equation solving equations subinterval Substituting successive approximations Suppose system of equations tangent terval tion tortoise Vlog x-axis Xn+1 y-axis y₁ α₁