A GENERIC AUTOMATIC NUMERICAL STABILITY TESTING METHOD

In this thesis we develop a new automatic method to test algorithm's numerical stability. The new method is a combination of two stability testing methods introduced by Higham and Kahan, and takes advantage of the both method. We first generate an objective function which can reveal algorithm's stability, then locate the maximum value of the objective function by an optimization method. This method can automatically detect the unstable points and reveal algorithms instability. To make our method suitable for general problems, we generate the objective function by measuring the difference of the test program's results computed in different rounding modes. We choose a search method suitable for our objective function. To improve the accuracy of our method, the final result is obtained by combining the results from multiple searches. F\lTthermore, we propose three measurements to measure algorithm's stability. Practical examples are used to test the performance of our method.