# The Mathematics of Numerical Analysis

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*James Renegar; Michael Shub; Steve Smale*

The lectures in this volume are the proceedings from the
1995 AMS-SIAM Summer Seminar in Applied Mathematics held in Park City,
UT. The mathematical theory of real number algorithms was the subject
of the conference, with emphasis on geometrical, algebraic, analytic,
and foundational perspectives. Investigations on efficiency played
a special role.

The goal of the conference was to give the topic of
numerical analysis greater coherence by focusing on the mathematical
side. Particular attention was aimed at strengthening the unity
of mathematics and numerical analysis and narrowing the gap between
pure and applied mathematics. The conference was international
in character, with strong representation from the most
mathematically developed parts of numerical analysis. Seminars in the
following areas were held: linear algebra, nonlinear systems-path
following, differential equations, linear programming, interval
arithmetic, algebraic questions, foundations, information based
complexity, lower bounds, and approximation theory.

#### Readership

Graduate students and research mathematicians interested in numerical analysis.