From the 1 of 11 linked papers with an AI index.
11 papers
Revisiting column subset selection through the lens of submodularity
Ilse C. F. Ipsen, Arvind K. Saibaba
The paper shows that the logarithm of the volume of a set of matrix columns is a submodular function, allowing classic QR with column pivoting to be viewed as a greedy algorithm wi…
Numerically Stable Cholesky-QR on GPU via Mixed-Precision Randomized Preconditioning
James E. Garrison, Chao Chen, Ilse C. F. Ipsen
Cholesky-QR is among the fastest algorithms for computing the thin QR factorization of tall-and-skinny matrices on GPUs, relying entirely on BLAS-3 operations. However, it is numer…
THE ROLE OF FOURIER ANALYSIS IN TWO DIMENSIONAL TOMOGRAPHY
Andre Mas, Fatma Terzioglu, Ilse C. F. Ipsen
We highlight the important role of the Fourier transform in deriving inversion formulas for the integral transforms of tomographic imaging. We demonstrate this principle by derivin…
Many (most?) column subset selection criteria are NP hard for a few columns
Ilse C. F. Ipsen, Arvind K. Saibaba
We consider a variety of criteria for selecting k representative columns from a real mxn matrix A, when sufficiently few columns are required, i.e., 1<= k<= min{rank(A), m/3}. The…
Perturbation Analysis for Preconditioned Normal Equations in Mixed Precision
James E. Garrison, Ilse C. F. Ipsen
For real matrices of full column-rank, we analyze the conditioning of several types of normal equations that are preconditioned by a randomized preconditioner computed in lower pre…
Solution of Least Squares Problems with Randomized Preconditioned Normal Equations
Ilse C. F. Ipsen
We consider the solution of full column-rank least squares problems by means of normal equations that are preconditioned, symmetrically or non-symmetrically, with a randomized prec…