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