Jacobi eigenvalue algorithm

<p>In <a href="/facts/Numerical_linear_algebra/jnS6Tteb">numerical linear algebra</a>, the Jacobi eigenvalue algorithm is an <a href="/facts/Iterative_method/uKMAJhEh">iterative method</a> for the calculation of the <a href="/facts/Eigenvalue/8TjEoT8u">eigenvalues</a> and <a href="/facts/Eigenvector/8TjEoT8u">eigenvectors</a> of a <a href="/facts/Real_number/R02gw5Pb">real</a> <a href="/facts/Symmetric_matrix/08CGwjNl">symmetric matrix</a> (a process known as <a href="/facts/Matrix_diagonalization/y3MkyTCy">diagonalization</a>). It is named after <a href="/facts/Carl_Gustav_Jacob_Jacobi/4Syeauo5">Carl Gustav Jacob Jacobi</a>, who first proposed the method in 1846, but only became widely used in the 1950s with the advent of computers.
</p><p>This algorithm is inherently a <a href="/facts/Dense_matrix/FFtN0XjR">dense matrix</a> algorithm: it draws little or no advantage from being applied to a sparse matrix, and it will destroy sparseness by creating fill-in. Similarly, it will not preserve structures such as being <a href="/facts/Band_matrix/Iz803N35">banded</a> of the matrix on which it operates.
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Jacobi eigenvalue algorithm open-in-new

Jacobi eigenvalue algorithm