tag:blogger.com,1999:blog-8288194986820249216.post5157674470383148490..comments2024-03-22T05:09:17.789-07:00Comments on Abstract Heresies: A Floating-point ProblemJoe Marshallhttp://www.blogger.com/profile/03233353484280456977noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-8288194986820249216.post-45008469777496617572021-09-23T20:17:28.513-07:002021-09-23T20:17:28.513-07:00If you check back whether your answer obtained thr...If you check back whether your answer obtained through rational arithmetic does indeed solve the problem, it doesn't - multiplying the coefficient matrix with the solution vector gives a product which is [0 0] and not [1 0] as required in the problem given by the rhs vector. Keshava Prasad Halemanenoreply@blogger.comtag:blogger.com,1999:blog-8288194986820249216.post-45222613904146922942021-08-28T19:18:22.826-07:002021-08-28T19:18:22.826-07:00Take an eigenvalue decomposition of the original 2...Take an eigenvalue decomposition of the original 2x2 matrix. You will see that the smallest eigenvalue is well below the ~16 digits of relative precision of IEEE double floating point. Effectively singular in that representation so the result is as expected.Jasonhttps://www.blogger.com/profile/11354154005586759842noreply@blogger.com