64 citations · 414 across the 34 of their papers we have counts for
7 papers · 1 filter
Fundamental invariants of orbit closures
Peter Bürgisser, Christian Ikenmeyer
For several objects of interest in geometric complexity theory, namely for the determinant, the permanent, the product of variables, the power sum, the unit tensor, and the matrix…
On the condition of characteristic polynomials
Peter Buergisser, Felipe Cucker, Elisa Rocha Cardozo
We prove that the expectation of the logarithm of the condition number of each of the zeros of the characteristic polynomial of a complex standard Gaussian matrix is . This m…
Membership in moment polytopes is in NP and coNP
Peter Bürgisser, Matthias Christandl, Ketan D. Mulmuley +1
We show that the problem of deciding membership in the moment polytope associated with a finite-dimensional unitary representation of a compact, connected Lie group is in NP and co…
Computing the Chow variety of quadratic space curves
Peter Bürgisser, Kathlén Kohn, Pierre Lairez +1
Quadrics in the Grassmannian of lines in 3-space form a 19-dimensional projective space. We study the subvariety of coisotropic hypersurfaces. Following Gel'fand, Kapranov and Zele…
Condition length and complexity for the solution of polynomial systems
Diego Armentano, Carlos Beltrán, Peter Bürgisser +2
Smale's 17th problem asks for an algorithm which finds an approximate zero of polynomial systems in average polynomial time (see Smale 2000). The main progress on Smale's problem i…
A stable, polynomial-time algorithm for the eigenpair problem
Diego Armentano, Carlos Beltrán, Peter Bürgisser +2
We describe algorithms for computing eigenpairs (eigenvalue-eigenvector pairs) of a complex matrix . These algorithms are numerically stable, strongly accurate, and…