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lect10, Tue 02/11

Norms of vector and matrices, matrix condition number

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Reading assignment

For Thursday, read 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.

References for today’s lecture

Sections 2.8 (effect of roundoff errors) and 2.9 (norms and condition numbers) of the NCM book.

Outline

• Norm and condition number
  • Norm of a vector: (Euclidean) 2-norm, (Manhattan) 1-norm, infinity norm
  • Norm of a matrix
  • Theorems about norms
  • Condition number of a matrix
  • Sensitivity analysis of Ax = b [later]
• cs111 routines:
  • cs111.hilbert()
• numpy/scipy routines:
  • npla.norm()
  • npla.cond()