7 citations · 23 across the 8 of their papers we have counts for
8 papers
Free (rational) Derivation
Konrad Schrempf
By representing elements in free fields (over a commutative field and a finite alphabet) using Cohn and Reutenauer's linear representations, we provide an algorithmic construction…
Horner Systems: How to efficiently evaluate non-commutative polynomials (by matrices)
Konrad Schrempf
By viewing non-commutative polynomials, that is, elements in free associative algebras, in terms of linear representations, we generalize Horner's rule to the non-commutative (mult…
Primal-dual interior-point Methods for Semidefinite Programming from an algebraic point of view, or: Using Noncommutativity for Optimization
Konrad Schrempf
Since more than three decades, interior-point methods proved very useful for optimization, from linear over semidefinite to conic (and partly beyond non-convex) programming; despit…
Free Fractions: An Invitation to (applied) Free Fields
Konrad Schrempf
Long before we learn to construct the field of rational numbers (out of the ring of integers) at university, we learn how to calculate with fractions at school. When it comes to "n…
A Standard Form in (some) Free Fields: How to construct Minimal Linear Representations
Konrad Schrempf
We describe a standard form for the elements in the universal field of fractions of free associative algebras (over a commutative field). It is a special version of the normal form…
A Factorization Theory for some Free Fields
Konrad Schrempf
Although in general there is no meaningful concept of factorization in fields, that in free associative algebras (over a commutative field) can be extended to their respective free…
On the Factorization of Non-Commutative Polynomials (in Free Associative Algebras)
Konrad Schrempf
We describe a simple approach to factorize non-commutative (nc) polynomials, that is, elements in free associative algebras (over a commutative field), into atoms (irreducible elem…
Linearizing the Word Problem in (some) Free Fields
Konrad Schrempf
We describe a solution of the word problem in free fields (coming from non-commutative polynomials over a commutative field) using elementary linear algebra, provided that the elem…