Lecture 4 Summary

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Discussion of Strassen algorithm and other matrix-multiply algorithms that do better than O(m3).

New topic: accuracy and stability. Start with LU factorization, and give example where small roundoff error can lead to huge mistakes. The next few lectures will deal with, in reverse order (iii) how to improve LU (pivoting); (ii) how to define/characterize accuracy and stability of algorithms; (i) how to describe roundoff errors and computer arithmetic.

Overview of floating-point representations, focusing on the IEEE 754 standard.