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1.3. Sources of Error

1.3. Sources of Error. Two sources of numerical error. Round off error Truncation error. Round-off Error. Round off Error. Caused by representing a number approximately. Truncation Error. Truncation error. Error caused by truncating or approximating a mathematical procedure.

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1.3. Sources of Error

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  1. 1.3. Sources of Error

  2. Two sources of numerical error • Round off error • Truncation error

  3. Round-off Error

  4. Round off Error • Caused by representing a number approximately

  5. Truncation Error

  6. Truncation error • Error caused by truncating or approximating a mathematical procedure.

  7. Example of Truncation Error Taking only a few terms of a Maclaurin series to approximate If only 3 terms are used,

  8. secant line P tangent line Q Figure 1. Approximate derivative using finite Δx Another Example of Truncation Error Using a finite to approximate

  9. Another Example of Truncation Error Using finite rectangles to approximate an integral.

  10. Example 1 —Maclaurin series Calculate the value of with an absolute relative approximate error of less than 1%. 6 terms are required. How many are required to get at least 1 significant digit correct in your answer?

  11. Example 2 —Differentiation Find for using and The actual value is Truncation error is then, Can you find the truncation error with

  12. Example 3 — Integration Use two rectangles of equal width to approximate the area under the curve for over the interval

  13. Integration example (cont.) Choosing a width of 3, we have Actual value is given by Truncation error is then Can you find the truncation error with 4 rectangles?

  14. THE END

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