Katrijn Frederix

Learn More
In this paper an implicit (double) shifted QR-method for computing the eigenvalues of companion and fellow matrices will be presented. Companion and fellow matrices are Hessenberg matrices, that can be decomposed into the sum of a unitary and a rank 1 matrix. The Hessenberg, the unitary as well as the rank 1 structures are preserved under a step of the(More)
A new sparse spectral clustering method using linear algebra techniques is proposed. This method exploits the structure of the Laplacian to construct its approximation, not in terms of a low rank approximation but in terms of capturing the structure of the matrix. The approximation is based on the incomplete Cholesky decomposition with an adapted stopping(More)
In this paper we consider a class of hierarchically rank structured matrices, including some of the hierarchical matrices occurring in the literature, such as hierarchically semiseparable (HSS) and certain H ∈-matrices. We describe a fast O(r 3 n log(n)) and stable algorithm to transform this hierarchical representation into a so-called unitary-weight(More)
Solving integral equations results in linear system Ax = b. Solving integral equations results in linear system Ax = b. Solving integral equations results in linear system Ax = b. Time-consuming evaluation of integrals. Large, dense, full rank and no explicit structure. Solving integral equations results in linear system Ax = b. Time-consuming evaluation of(More)
In this paper we propose a method for computing the roots of a monic matrix polynomial. To this end we compute the eigenvalues of the corresponding block companion matrix C. This is done by implementing the QR algorithm in such a way that it exploits the rank structure of the matrix. Because of this structure, we can represent the matrix in Givens-weight(More)
  • K C A M Luyben, Rector Magnificus, C Vuik, M B Van Gijzen, Boley, B Szyld +48 others
  • 2011
Acknowledgments This dissertation concludes four years of intense scientific research in the numerical analysis group at Delft University of Technology. It was an unforgettable experience and I learned many valuable lessons, both personally and professionally. I would not have been able to finish such a large body of work without the help of many people,(More)
In this paper two fast algorithms that use orthogonal similarity transformations to convert a symmetric rationally generated Toeplitz matrix to tridiagonal form are developed, as a means of finding the eigenvalues of the matrix efficiently. The reduction algorithms achieve cost efficiency by exploiting the rank structure of the input Toeplitz matrix. The(More)
An efficient algorithm for the direct solution of a linear system associated with the discretization of boundary integral equations with oscillatory kernels (in two dimensions) is described without having to compute the complete matrix of the linear system. This algorithm is based on the unitary-weight representation, for which a new construction based on(More)
  • Rob H Bisseling, Karma Dajani Tammo, Jan Dijkema, Johan Van De Leur, Paul A Zegeling, Rob Bisseling +50 others
  • 2007
Locally in the Netherlands, this study group is also known as the Studieweek Wiskunde en Industrie 2007 (SWI2007). During the week of the study group, 79 participants tried to solve six problems with a high mathematical content posed to them by industry. Most (but not all) of the participants were mathematicians , mainly from the Netherlands and Belgium,(More)
  • 1