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lect11, Thu 02/13

How floating-point works

• Lecture Files

Reading assignment

For next week, read NCM Sections 10.1, 10.2, and 10.5, and “The $25,000,000,000 Eigenvector”.

References for today’s lecture

Section 1.7 (floating-point arithmetic) of the NCM book, and this Wikipedia page on floating-point format.

You may also want to look at this nice article on the IEEE 64-bit floating-point standard by John Cook. Also, here is an interesting article on Google’s TPU processor, which uses a different floating-point format.

Outline

• A few more words about matrix condition number

• Floating-point arithmetic

• Backward error analysis and error bounds on partial pivoting [didn’t get to this]

• cs111 routines:
  • cs111.print_float64()
• numpy/scipy objects and routines:
  • np.float64
  • np.finfo()
  • np.inf
  • np.nan
  • np.isinf()
  • np.isnan()