4. Euclidean methods
This section introduces geometric methods for solving linear equations, both from an exact and approximate point of view (through the concept of pseudo-solutions). The methods of Jacobi, bisection and iterated QR are intended for the calculation of eigenvalues and are covered in another article.
We'll consider a real or complex Euclidean vector space E of dimension n, i.e., a vector space provided with a scalar product and the norm derived from it. We'll note (x½y) the scalar product of two vectors x and y and the norm of a vector x (it's actually N 2 (x )). If an orthonormal basis (e 1 ,..., e ...
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Euclidean methods
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The actual implementation of the methods described above requires highly precise computer techniques which the size of this article does not allow us to cover. In any case, "off-the-shelf" programs are not always well-suited to real-life situations, which may require prior simplifications, estimates of tolerable errors, etc.
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