[Reliable Computing] a new book with a strong emphasis on interval methods

The following book describes complex interval arithmetic and new
techniques that use this arithmetic to produce guaranteed estimates for
the roots.
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Miodrag Petkovic, "Point Estimation of Root Finding Methods", Springer
Lecture Notes in Mathematics, Vol. 1933, 2008 

Product Description

This book sets out to state computationally verifiable initial
conditions for predicting the immediate appearance of the guaranteed and
fast convergence of iterative root finding methods. Attention is paid to
iterative methods for simultaneous determination of polynomial zeros in
the spirit of Smale's point estimation theory, introduced in 1986. Some
basic concepts and Smale's theory for Newton's method, together with its
modifications and higher-order methods, are presented in the first two
chapters. The remaining chapters contain the recent author's results on
initial conditions guaranteeing convergence of a wide class of iterative
methods for solving algebraic equations. 

These conditions are of practical interest since they depend only on
available data, the information of a function whose zeros are sought and
initial approximations. The convergence approach presented can be
applied in designing a package for the simultaneous approximation of
polynomial zeros.