This is a self-contained textbook that offers a rigorous presentation of numerical analysis, at a medium level of training in mathematics. The reader can find proofs of the important results and technical details relevant for applications, as well as interesting information about the historical background or advanced concepts in modern analysis. The exposition style is attractive, and theoretical aspects are illustrated by carefully selected exercises (with solutions). The material is structured in 19 chapters, as follows: 1. Numerical algorithms, 2. Nonlinear equations, 3. Linear systems, 4. Direct solvers, 5. Vector spaces, 6. Operators, 7. Nonlinear systems, 8. Iterative methods, 9. Conjugate gradients, 10. Polynomial interpolation, 11. Chebyshev and Hermite interpolation, 12. Approximation theory, 13. Numerical quadrature, 14. Eigenvalue problems, 15. Eigenvalue algorithms, 16. Ordinary differential equations (ODEs), 17. Higher-order ODE discretization methods, 18. Floating point, 19. Notation. The book is recommended to students and researchers whose interests go beyond “successful recipes”, towards consistent insights into the mathematical support.

Reviewer:

Octavian Pastravanu (Iaşi)