caa a22 4500 463183940 CHVBK 20180406164846.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s10492-007-0005-6 doi (NATIONALLICENCE)springer-10.1007/s10492-007-0005-6 Rohn Jiří Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou věží 2, 182 07, Prague 8, Czech Republic aut Nonsingularity, positive definiteness, and positive invertibility under fixed-point data rounding [Elektronische Daten] [Jiří Rohn] For a real square matrix A and an integer d ⩾ 0, let A (d) denote the matrix formed from A by rounding off all its coefficients to d decimal places. The main problem handled in this paper is the following: assuming that A (d) has some property, under what additional condition(s) can we be sure that the original matrix A possesses the same property? Three properties are investigated: nonsingularity, positive definiteness, and positive invertibility. In all three cases it is shown that there exists a real number α(d), computed solely from A (d) (not from A), such that the following alternative holds if d > α(d), then nonsingularity (positive definiteness, positive invertibility) of A (d) implies the same property for A if d < α(d) and A (d) is nonsingular (positive definite, positive invertible), then there exists a matrix A′ with A′(d) = A (d) which does not have the respective property. For nonsingularity and positive definiteness the formula for α(d) is the same and involves computation of the NP-hard norm ‖ · ‖∞,1; for positive invertibility α(d) is given by an easily computable formula. Mathematical Institute, Academy of Sciences of Czech Republic, 2007 nonsingularity nationallicence positive definiteness nationallicence positive invertibility nationallicence fixed-point rounding nationallicence Applications of Mathematics Kluwer Academic Publishers-Consultants Bureau 52/2(2007-04-01), 105-115 0862-7940 52:2<105 2007 52 10492 https://doi.org/10.1007/s10492-007-0005-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10492-007-0005-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rohn Jiří Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou věží 2, 182 07, Prague 8, Czech Republic aut NATIONALLICENCE 773 0- Applications of Mathematics Kluwer Academic Publishers-Consultants Bureau 52/2(2007-04-01), 105-115 0862-7940 52:2<105 2007 52 10492 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer