I can predict when this will happen by looking at the magnitude of the condition number estimator, but I don't have a good solution for what to do when it occurs.
42.
The explicit use of the product \ mathbf { V } ^ { * } \ mathbf { V } makes the algorithm unstable, especially if the product's condition number is large.
43.
The Serbian government reservedly accepted all of the conditions of the ultimatum, except for condition number six which demanded the inclusion of Austria-Hungary in Serbia's judicial inquiry into the assassination.
44.
In comparison, the relative error bound for naive summation ( simply adding the numbers in sequence, rounding at each step ) grows as O ( \ varepsilon n ) multiplied by the condition number.
45.
T " X ", is very ill-conditioned ( i . e . if its condition number multiplied by the machine's relative round-off error is appreciably large ).
46.
The condition number of the problem is the ratio of the relative error in the function's output to the relative error in the input, and varies with both the function and the input.
47.
Under such circumstances x _ { k } converges exponentially fast to the solution of Ax = b, and the rate of convergence depends only on the scaled condition number \ kappa ( A ).
48.
The goal of this preconditioned system is to reduce the condition number of the left or right preconditioned system matrix P ^ {-1 } A or AP ^ {-1 }, respectively.
49.
He has more than 85 refereed publications on topics such as rounding error analysis, linear systems, least squares problems, matrix functions and nonlinear matrix equations, condition number estimation, and generalized eigenvalue problems.
50.
If the condition number is not too much larger than one ( but it can still be a multiple of one ), the matrix is well conditioned which means its inverse can be computed with good accuracy.
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