Please use this identifier to cite or link to this item: http://repositorio.inesctec.pt/handle/123456789/6595
Title: Typing linear algebra: A biproduct-oriented approach
Authors: Macedo,HD
José Nuno Oliveira
Issue Date: 2013
Abstract: Interested 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.
URI: http://repositorio.inesctec.pt/handle/123456789/6595
http://dx.doi.org/10.1016/j.scico.2012.07.012
metadata.dc.type: article
Publication
Appears in Collections:HASLab - Articles in International Journals

Files in This Item:
File Description SizeFormat 
P-006-6G1.pdf530.36 kBAdobe PDFThumbnail
View/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.