3 papers
math.CO2020
On the explicit formula for Gauss-Jordan elimination
Nam Van Tran, Julia Justino, Imme van den Berg
The elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure have the form of quotients of minors. Instead of the proof using identities of determ…
math.CO2020
The explicit formula for Gauss-Jordan elimination and error analysis
Nam Van Tran, Júlia Justino, Imme van den Berg
The explicit formula for the elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure for the solution of systems of linear equations is applied t…
math.RA2019
An algebra for the propagation of errors in matrix calculus
Nam van Tran, Imme van den Berg
We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter…