Atkinson K., Han W. Theoretical Numerical Analysis... 2ed 2005

Textbook in PDF format

The book presents an abstract point of view of Numerical Analysis (as one can immediatly see by the title!). It is written by a master in the topic, author of more than 70 publications at the higher levels, well known for his contributions in Integral and Partial Differential Equations.
If one is interested on the basic aspects of numerical analysis, I also suggest to consider his well known manual "Elementary Numerical Analysis".
The present book presents several aspects that are not covered by most of the manuals in Numerical Analysis and highly contributes to have a wider idea of convergence and stability of some well known methods