...one of the most highly
regarded and expertly designed C++ library projects in the
world. — Herb Sutter and Andrei
By and large the performance of this library should be acceptable for most needs. However, you should note that this library's primary emphasis is on accuracy and numerical stability, and not speed.
In terms of the algorithms used, this library aims to use the same "best of breed" algorithms as many other libraries: the principle difference is that this library is implemented in C++ - taking advantage of all the abstraction mechanisms that C++ offers - where as most traditional numeric libraries are implemented in C or FORTRAN. Traditionally languages such as C or FORTRAN are perceived as easier to optimise than more complex languages like C++, so in a sense this library provides a good test of current compiler technology, and the "abstraction penalty" - if any - of C++ compared to other languages.
The two most important things you can do to ensure the best performance from this library are:
The performance section contains more information on the performance of this library, what you can do to fine tune it, and how this library compares to some other open source alternatives.