7 citations · 20 across the 8 of their papers we have counts for
9 papers
On non-linear optimization with a perturbed objective function
Nam Van Tran, Imme van den Berg
A Lagrange multiplier theorem is derived for the case of an imprecise objective function and a precise constraint. The proof uses methods of analysis which deal in a direct, algebr…
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…
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…
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…
On flexible sequences
Bruno Dinis, Tran Van Nam, Imme van den Berg
In the setting of nonstandard analysis we introduce the notion of flexible sequence. The terms of flexible sequences are external numbers. These are a sort of analogue for the clas…
Axiomatics for the external numbers of nonstandard analysis
Bruno Dinis, Imme van den Berg
Neutrices are additive subgroups of a nonstandard model of the real numbers. An external number is the algebraic sum of a nonstandard real number and a neutrix. Due to the stabilit…