The question behind the paper is simple to state:<\/p>\n\n\n\n
Can additional mathematical structure turn a problem that is not computable in general into one that is computable?<\/em><\/strong><\/p>\n\n\n\n In numerical linear algebra, we often exploit symmetry to transform a whole class of matrices into a simpler block-diagonal form. In computable analysis, however, even basic quantities such as the rank of a real matrix can fail to be computable when the matrix is given only through arbitrarily accurate approximations.<\/p>\n\n\n\n In this paper, I show that for matrix classes arising from finite-group symmetries, the group structure provides enough discrete information to overcome this obstruction and uniformly compute the relevant isotypic block decomposition.<\/p>\n\n\n\n The paper also connects this construction with structured QR and QX factorizations, including the centrosymmetric case that I worked on previously.<\/p>\n\n\n\n Preliminary results from this work were presented at CCA 2026<\/a> in Trier.<\/p>\n\n\n\n arXiv:<\/strong> 2610.02547 <\/p>\n
https:\/\/arxiv.org\/abs\/2610.02547<\/a><\/p>\n\n\n\n
