This paper presents AutoDJ: a system for automatically gene rati g music playlists based on one or more seed songs selected by a use r. A toDJ uses Gaussian Process Regression to learn a userâ€¦ (More)

It is known that without pivoting Gaussian elimination can run significantly faster, particularly for matrices that have structure of Toeplitz or Hankel types, but becomes numerically unsafe. Theâ€¦ (More)

Solution of homogeneous linear systems of equations is a basic operation of matrix computations. The customary algorithms rely on pivoting, orthogonalization and SVD, but we employ randomizedâ€¦ (More)

We propose new effective randomized algorithms for some fundamental matrix computations such as preconditioning of an ill conditioned matrix that has a small numerical nullity or rank, its 2-by-2â€¦ (More)

It is known that pivoting-free Gaussian elimination is numerically unsafe but can run significantly faster than GEPP. We prove and confirm experimentally that randomized preconditioning combined withâ€¦ (More)

Random matrices tend to be well conditioned, and so one can expect that appending properly scaled random rows and columns or adding a scaled random matrix of a fixed rank can decrease the conditionâ€¦ (More)

Effective preconditioners are known for some important but special classes of matrices. In contrast our properly scaled randomized additive preprocessing and augmentation are likely to preconditionâ€¦ (More)

Abstract. An adaptive finite element method is presented for the elastic scattering of a timeharmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into aâ€¦ (More)

We review and amend the known applications of Newtonâ€™s iteration computing the inverse or Mooreâ€“Penrose generalized inverse of a matrix. Then we specialize this approach to the case of structuredâ€¦ (More)