COS126_Lecture11-12_Scientific_Computation notes

COS126_Lecture11-12_Scientific_Computation notes - Lecture...

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No notes today due to the written exam. Lecture 11 - Written Exam 1 Tuesday, March 12, 2013 10:00 AM COS 126 - General Computer Science Page 1
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Lecture 12... Audio recording started: 10:02 AM Thursday, March 14, 2013 Use of doubles in scientific computing ensures that we have the necessary accuracy. IEEE 754 is a tree (or representation?) Float is 32-bits (less precision) and double is 64-bits (more precision) We use biases to represent negative numbers properly (basically just a trick). Sign bit is first bit (we will utilize that 1/2 is 0.1 in binary then we go to 1/4 then 1/8 etc… Pi cannot be represented accurately (exactly) - binary can come close, but not get it exactly Note that float cuts precision (making numbers appear as we'd like them to even if it's incorrect). The nearest floating point agrees to as many decimal points that doubles are able to do (only 16 decimal places). Catastrophic cancellation occurs during subtraction as many significant digits get lost - this poses problems (even in real life).
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  • Fall '08
  • Scientific Computing, upper triangular form, general computer science, Science Page

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