This is Paul Breiding's talk "What is ... a Condition Number?" at the "What is ...?" seminar. The talk was given on Friday, July 7, 2017, 1:00pm in the BMS Lounge at TU Berlin.
In this talk I will motivate and introduce a fundamental notion in numerical analysis - the condition number. Condition numbers serve as a measure of how sensitive a function is with respect to perturbations in the input. I will give an introductory example demonstrating that small changes in the input data may lead to large deviations in the output even for seemingly simple problems such as solving linear equation. Using this example I will give the definition of condition number and then go over to define condition numbers à la Shub and Smale within a more general framework.
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