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for solving least squares problems, these problems can also be solved by methods that include the Gram-Schmidt algorithm and Householder methods.

Conditioning and stability

Allow that a problem is a function , where X is a normed vector space of data and Y is a normed vector space of solutions. For some data point , the problem is said to be ill-conditioned if a small perturbation in x produces a large change in the value of f(x). We can quantify this by defining a condition number which

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