The trust region subproblem is solved by the truncated conjugate gradient method described in Powell did not write a report on the other details of LINCOA.
42.
Iterative methods, such as conjugate gradient method and GMRES utilize fast computations of matrix-vector products Ax _ i, where matrix A is sparse.
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Lasso regularized models can be fit using a variety of techniques including subgradient methods, least-angle regression ( LARS ), and proximal gradient methods.
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In mathematics, more specifically in numerical linear algebra, the "'biconjugate gradient method "'is an algorithm to solve systems of linear equations
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The conjugate gradient method can be derived from several different perspectives, including specialization of the conjugate direction method for optimization, and variation of the Lanczos iteration for eigenvalue problems.
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*PM : extended discussion of the conjugate gradient method, id = 9859 new !-- WP guess : extended discussion of the conjugate gradient method-- Status:
47.
*PM : extended discussion of the conjugate gradient method, id = 9859 new !-- WP guess : extended discussion of the conjugate gradient method-- Status:
48.
Unlike the conjugate gradient method, this algorithm does not require the matrix A to be self-adjoint, but instead one needs to perform multiplications by the conjugate transpose.
49.
In such cases, the step calculation itself will typically need to be done with an approximate iterative method appropriate for large and sparse problems, such as the conjugate gradient method.
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This makes direct solution of the system of linear equations quite costly ( although efficient approximate solutions exist, for example use of the conjugate gradient method preconditioned with incomplete Cholesky factorization ).
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