| 21. | The Schur complement, however, has condition number only of the order 1 / " h ".
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| 22. | However, the condition number does not give the exact value of the maximum inaccuracy that may occur in the algorithm.
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| 23. | For example, the 2-norm condition number of the matrix above is about 4.8 ?10 5.
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| 24. | However the downside of forming the normal equations is that the condition number ? ( "'A "'
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| 25. | An algorithm is " forward stable " if its forward error divided by the condition number of the problem is small.
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| 26. | The condition number of the mostly used functions are as follows; these can be used to compute significant figures for all elementary functions:
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| 27. | P of a matrix A is a matrix such that P ^ {-1 } A has a smaller condition number than A.
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| 28. | On the other hand, for random inputs with nonzero mean the condition number asymptotes to a finite constant as n \ to \ infty.
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| 29. | For very high condition numbers, even very small errors due to rounding can be magnified to such an extent that the result is meaningless.
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| 30. | Essentially, the condition number represents the " intrinsic " sensitivity of the summation problem to errors, regardless of how it is computed.
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