With respect to the previous editions (see the reviews in Zbl 0913.65002, Zbl 0943.65001, Zbl 1136.65002), the fourth edition of this book (in Italian) presents one more chapter and many topics which are revised in order to make them clearer. The book deals with classical subjects in numerical analysis: elements of numerical linear algebra, foundations of numerical analysis (numerical stability, condition numbers and error analysis), direct and iterative methods for linear systems, numerical approximation of eigenvalues and eigenvectors, numerical methods for nonlinear equations (in particular polynomials) and nonlinear systems, polynomial interpolation (including splines), numerical methods for integration (including adaptive methods and methods for multidimensional integrals), basic concepts of the theory of orthogonal polynomials and trigonometric approximation and numerical approximation of derivatives, numerical solution of ordinary differential equations and approximation of limit problems (including basic concepts of finite element methods), numerical methods for partial differential equations of parabolic and hyperbolic types (including the finite element approach).
The style is modern and rich. The bibliography is reduced with respect to the previous editions and contains 77 references, whereas the list of available MATLAB programs is very long and contains 92 items. This makes the book not only a remarkable textbook, but also a helpful tool for researchers in various fields needing computational methods. Moreover, many illustrating examples and case studies are presented together with a large collection of exercises.