...Vincent A. Barker1
Department of Mathematical Modelling (IMM), Technical University of Denmark, Building 305, DK-2800 Lyngby, Denmark; email: vab@imm.dtu.dk 
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... Blackford2
Department of Computer Science, University of Tennessee, 1122 Volunteer Blvd., Suite 203, Knoxville, TN 37996-3450, USA; email susan@cs.utk.edu 
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... Jack J. Dongarra3
Department of Computer Science, University of Tennessee, 1122 Volunteer Blvd., Suite 203, Knoxville, TN 37996-3450, USA; email: dongarra@cs.utk.edu 
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... Jeremy Du Croz4
Numerical Algorithms Group Ltd, Wilkinson House, Jordan Hill Road, Oxford OX2 8DR, UK; email: jeremy@nag.co.uk 
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... Sven Hammarling5
Numerical Algorithms Group Ltd, Wilkinson House, Jordan Hill Road, Oxford OX2 8DR, UK; email: sven@nag.co.uk 
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... Minka Marinova6
The Danish Computing Center for Research and Education (UNI$\bullet$C), Technical University of Denmark, Lyngby, Denmark; Email: Minka.Marinova@uni-c.dk 
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...sniewski7
The Danish Computing Center for Research and Education (UNI$\bullet$C), Technical University of Denmark, Bldg. 304, DK-2800 Lyngby, Denmark; Email: jerzy.wasniewski@uni-c.dk 
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... Yalamov8
Center of Applied Mathematics and Informatics, University of Rousse, Bulgaria; Email: yalamov@ami.ru.acad.bg 
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... defined2.1
If we tried to compute the trivial eigenvalues in the same way as the nontrivial ones, that is by taking ratios of the leading $n-r$ diagonal entries of $X^T A^T AX$ and $X^T B^T B X$, we would get 0/0. For a detailed mathematical discussion of this decomposition, see the discussion of the Kronecker Canonical Form in [19]. 
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... output)3.1
(Input or output) means that the argument may be either an input argument or an output argument, depending on the values of other arguments. For example, in the xyySVX driver routines, some arguments are used either as output arguments to return details of a factorization, or as input arguments to supply details of a previously computed factorization. 
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... )6.1
wp ::= KIND( 1.0) $\mid$ KIND( 1.0D0) 
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... 6.2
wp ::= KIND( 1.0) $\mid$ KIND( 1.0D0) 
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... )7.1
wp is a work precision; wp ::= KIND( 1.0) $\mid$ KIND( 1.0D0) 
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... )7.2
wp ::= KIND( 1.0) $\mid$ KIND( 1.0D0) 
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... )7.3
wp ::= KIND( 1.0) $\mid$ KIND( 1.0D0) 
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... )7.4
wp ::= KIND( 1.0) $\mid$ KIND( 1.0D0) 
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... )7.5
wp is a work precision; wp ::= KIND( 1.0) $\mid$ KIND( 1.0D0) 
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... )8.1
wp ::= KIND( 1.0) $\mid$ KIND( 1.0D0) 
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... )8.2
wp ::= KIND( 1.0) $\mid$ KIND( 1.0D0) 
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