Rump, Siegfried M.Siegfried M.Rump2021-02-102021-02-102003-01-01IMA Journal of Numerical Analysis 1 (23): 1-9 (2003-01-01)http://hdl.handle.net/11420/8727We give lower and upper bounds for the optimal p-norm condition number achievable by two-sided diagonal scalings. There are no assumptions on the irreducibility of certain matrices. The bounds are shown to be optimal for the 2-norm. For the 1-norm and inf-norm the (known) exact value of the optimal condition number is confirmed. We give means how to calculate the minimizing diagonal matrices. Furthermore, a class of new lower bounds for the componentwise distance to the nearest singular matrix is given. They are shown to be superior to existing ones.en1464-36422003119Oxford Univ. PressComponentwise distance to singularityCondition number, p-normInterval matrixOptimal scalingStrongly regularInformatikMathematikTechnikJournal Article10.1093/imanum/23.1.1Other