Please use this identifier to cite or link to this item: http://repositorio.inesctec.pt/handle/123456789/6595
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dc.contributor.authorMacedo,HDen
dc.contributor.authorJosé Nuno Oliveiraen
dc.date.accessioned2018-01-17T10:09:30Z-
dc.date.available2018-01-17T10:09:30Z-
dc.date.issued2013en
dc.identifier.urihttp://repositorio.inesctec.pt/handle/123456789/6595-
dc.identifier.urihttp://dx.doi.org/10.1016/j.scico.2012.07.012en
dc.description.abstractInterested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category with biproducts. This shifts the traditional view of matrices as indexed structures to a type-level perspective analogous to that of the pointfree algebra of programming. The derivation of fusion, cancellation and abide laws from the biproduct equations makes it easy to calculate algorithms implementing matrix multiplication, the central operation of matrix algebra, ranging from its divide-and-conquer version to its vectorization implementation. From errant attempts to learn how particular products and coproducts emerge from biproducts, not only blocked matrix algebra is rediscovered but also a way of extending other operations (e.g. Gaussian elimination) blockwise, in a calculational style, is found. The prospect of building biproduct-based type checkers for computer algebra systems such as MATLAB (TM) is also considered.en
dc.languageengen
dc.relation5601en
dc.rightsinfo:eu-repo/semantics/openAccessen
dc.titleTyping linear algebra: A biproduct-oriented approachen
dc.typearticleen
dc.typePublicationen
Appears in Collections:HASLab - Articles in International Journals

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