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Logarithm of the product of numbers, complex case
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Classroom Contents
Tricks and Tips in Numerical Computing - Keynote
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- 1 Welcome
- 2 Introducing the speaker
- 3 What are tricks and tips?
- 4 Differentiation with(out) a difference
- 5 V-shape curve is a result of floating-point evaluation (cancelation) errors dominating truncation errors
- 6 "Automatic differentiation "
- 7 Complex step method
- 8 Example: derivative of atan(x)/(1 + e^(-x^2)) at x = 2
- 9 Computing principal logarithm in a complex plane, a multi-valued function
- 10 Computing the principle logarithm in the 1960s
- 11 Logarithm of the product of numbers, complex case
- 12 Arcsin and Arccos in complex plane
- 13 Unwinding number
- 14 Roundtrip relations
- 15 Accurate difference
- 16 Low rank updated of n x n real matrix A
- 17 Why Sherman-Morrison formula holds?
- 18 World's Most Fundamental Matrix Equation
- 19 Computing a product
- 20 Matrix chain multiplication problem (MCMP)
- 21 Chain rule of differentiation and MCMP
- 22 Randomization
- 23 1985 IEEE Standard 754 and it 2008 Revision
- 24 Model for rounding errors analysis
- 25 This model is weaker than what IEEE Standard actually says
- 26 Model vs correctly rounded result
- 27 Prevision versus accuracy
- 28 Accuracy is not limited by the precision
- 29 Photocopying errors
- 30 Typing errors
- 31 Low precision arithmetic
- 32 Applications of half-precision (fp16, floating point 16 bits)
- 33 Error analysis in low precision arithmetic
- 34 What you can do to reduce error in fp16?
- 35 Can we obtain more information bounds?
- 36 Conclusions
- 37 Q&A: how to avoid the case when randomization makes the problem worse?
- 38 Q&A: how to choose between methods like contour integral and higher precision arithmetic?
- 39 Q&A: does half-precision allow a brute force analysis of the distribution of operations?
- 40 Q&A: can you comment on low precision and power consumption?
