Condition and Numerical Algorithms

Numerical algorithms are performed in finite-precision. Each arithmetic operation is affected by an error and the accumulation of these errors may end up in grossly inaccurate outputs. Central to the study of the precision needed to ensure meaningful outputs is the notion of condition of a data, a notion that turns out to control as well the speed of convergence of iterative algorithms. In the talk I will explain in detail these notions, provide numerous examples, and point out the differences with symbolic algorithms.