Software Open Access

# Shift Block Recycled GMRES: A Sylvester equation based minimum residual Krylov subspace method for solving multiple shifted systems

Soodhalter, Kirk M.

### DataCite XML Export

<?xml version='1.0' encoding='utf-8'?>
<identifier identifierType="DOI">10.5281/zenodo.56157</identifier>
<creators>
<creator>
<creatorName>Soodhalter, Kirk M.</creatorName>
<givenName>Kirk M.</givenName>
<familyName>Soodhalter</familyName>
<affiliation>Johannes Kepler University</affiliation>
</creator>
</creators>
<titles>
<title>Shift Block Recycled Gmres: A Sylvester Equation Based Minimum Residual Krylov Subspace Method For Solving Multiple Shifted Systems</title>
</titles>
<publisher>Zenodo</publisher>
<publicationYear>2016</publicationYear>
<subjects>
<subject>Krylov subpace methods</subject>
<subject>shifted systems</subject>
<subject>Sylvester equations</subject>
<subject>GMRES</subject>
<subject>augmented methods</subject>
<subject>subspace recycling</subject>
</subjects>
<dates>
<date dateType="Issued">2016-05-17</date>
</dates>
<resourceType resourceTypeGeneral="Software"/>
<alternateIdentifiers>
<alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/56157</alternateIdentifier>
</alternateIdentifiers>
<rightsList>
<rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
</rightsList>
<descriptions>
<description descriptionType="Abstract">&lt;p&gt;We propose a block Krylov subspace method for solving a family of shifted linear systems based on the GCRO-DR method proposed in [Parks et al. SISC 2005], which is an iterative method allowing for the efficient minimization of the the residual over an augmented block Krylov subspace. It has been previously shown that using augmented methods to solve multiple shifted systems simultaneously can been problematic for non-symmetric problems.&amp;nbsp; Here, this difficulty is overcome by using the Sylvester equation formulation of a family of shifted systems and applying a block Krylov subspace method to solve this Sylvester equation (a strategy proposed by Simoncini in 1996).&amp;nbsp; This strategy is fully compatible with augmentation and, specifically, with a GCRO-type minimization method.&lt;/p&gt;</description>
<description descriptionType="Other">Associated to the paper: Block Krylov Subspace Recycling for Shifted Systems with Unrelated Right-Hand Sides (Kirk M. Soodhalter), In SIAM Journal on Scientific Computing, volume 38, 2016.</description>
</descriptions>
</resource>