# Numerical Solution of Equations

• I. P. Mysovskih
Chapter

## Abstract

In this chapter, methods for the numerical solution of equations of the form
$$P\left( x \right)=0,$$
will be considered, where P(x) is in general a complex-valued function. Although it is true that an “explicit” solution of this equation may be given in certain very rare cases, even so, the formulas which are obtained for this are ordinarily very involved and consequently difficult to use. Because of this, it is of considerable importance to have methods for finding approximate solutions of the equation considered. The following numerical methods for the solution of equations will be presented below: The secant (chord) method, the method of iterations, Newton’s method, Lobačevskiĭ’s method, and factorization methods, including Lin’s method. The method of iterations and Newton’s method will also be given for systems of equations.

## Keywords

Initial Approximation Modify Form Real Solution Factorization Method Decimal Place
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