• 2007-02-14: assignments from Russ

Problems

1.4

• 16 points
• question sees if you understand how to compute absolute error for an expression.
  • reguritation - can you come up with the right formula? 3 points a,b,c
  • analysis - can you determine what is important about the formula? 3 points overall
  • comprehension - can you figure out what the formula mean? 4 points
    • exclude zero 1
    • include negatives 1
    • get multples of pi 2
• using exact numbers -3
• not reducing error expressions -3
• not explaining why for part d -4
• Using only first term of taylor series expansion for sin(x) -2
• incorrect use of formula for cond -2
• using formula for cond, but not simplifiying other parts (?) -2
• bounding numerator sin and cos by 1 (ok in my book)

1.6

• 9 points
• not giving enough significant digits to judge the problem as correct ( -0.0000 )

1.9

• 16 points
• ability to compute forward error 4
• realization that part c is more accurate. 4
• relationship between truncation error being smaller than cancellation error 4
  • no explanation: -4
• realization that this phenominon happens at epsilon machine 4
  • missing the explanations entirely, no mention of epsilon machine -4
  • just mention epsilon machine: -2
  • forget h/r: -1

1.9 b

• 16 points
• ability to compute forward error 4
• realization that the exact value is more correct 4
• explanation of why (truncation error) 4
  • mention truncation error 2
  • explain 2
• tried it on a computer 2
• give an h and a justification 2 or
• show coherent computer plot

1.12

• 9 points
• only picking up rounding error, missing cancellation error -6
• only picking up on cancellation error, missing rounding error (ok in my book)

1.4

• 16 points
  • 4 doing assignment
  • 5 showing error
  • 5 explanation
  • 2 graph and output problems

1.6

• 16 points
  • 8 explanation
  • 4 code
  • 4 example

1.7

• 18 points
  • 3 for attempt
  • 5 for explanation
  • 10 for graph
    • -3 for log log, etc.