1. Mathematical Preliminaries
Korea University
Computer Graphics Lab.
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2. Floating Point Number
부동 소수(Floating point number)는 부호(sign), 가수(mantissa), 지수(characteristic)로 이루어진다.
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3. Representation Range
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4. Normalization
Normalize: 지수가 표현하는 범위 안으로 가수 부분을 제한한다.
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5. IEEE Standard s: 부호 (1 bit) c: 지수 (11 bits) f: 가수 (52 bits)
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6. Chopping, Rounding and Roundoff Error
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7. Example 1
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8. Absolute and Relative Errors
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9. Significant Digits (1/2)
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10. Significant Digits (2/2)
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11. Example 3 (1/2)
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12. Example 3 (2/2)
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13. Cancellation Error
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14. Example 5 (1/4)
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15. Example 5 (2/4)
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16. Example 5 (3/4)
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17. Example 5 (4/4)
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18. Example 6 (1/3)
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19. Example 6 (2/3)
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20. Example 6 (3/3)
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21. Algorithms and Convergence
An algorithm is a procedure that describes,
In an unambiguous manner,
A finite sequence of steps
To be performed in a specified order.
A pseudocode is used for describing the algorithms.
Specifies the form of the input to be supplied and the form of the desired output.
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22. Example 1
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23. Stable or Unstable Algorithms
Stable Algorithm is that
Small changes in the initial data produce correspondingly small changes in the final results.
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24. Example 3 (1/4)
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25. Example 3 (2/4)
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26. Example 3 (3/4)
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27. Example 3 (4/4)
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28. Rate of Convergence (sequence)
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29. Example 4 (1/2)
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30. Example 4 (2/2)
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31. Rate of Convergence (function)
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32. Example 5
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