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Analysis of the truncated conjugate gradient method for linear matrix equations.(English)Zbl 1515.65096

Summary: The matrix-oriented version of the conjugate gradient (CG) method can be used to approximate the solution to certain linear matrix equations. To limit memory consumption, low-rank reduction of the factored iterates is often employed, possibly leading to disruption of the regular convergence behavior. We analyze the properties of the method in the matrix regime and identify the quantities that are responsible for early termination, usually stagnation, when truncation is in effect. Moreover, we illustrate relations between CG and a projection technique directly applied to the same matrix equation.

MSC:

65F45 Numerical methods for matrix equations
65F55 Numerical methods for low-rank matrix approximation; matrix compression

Software:

Matlab

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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