(a) (b) (c) Figure: (a) In a simple blocked low rank approximation the diagonal blocks are dense (gray), whereas the off-diagonal blocks are low rank. (b) In an HODLR matrix the low rank off-diagonal blocks form a hierarchical structure leading to a much more compact representation. (c) H2 matrices are a refinement of this idea. (a) In simple blocked low rank approximation the diagonal blocks a...

The Carlitz rank of a permutation polynomial f over a finite field Fq is a simple concept that was introduced in the last decade. Classifying permutations over Fq

This paper applies conventional tests (Johansen, 1995) and new tests (Chao and Phillips,1999) for cointegration to long{run money demand functions using Canadian data from 1872 to 1997. If cointegration is found, recently proposed tests by Quintos (1997) for stability of the cointegration rank are carried out. The paper focuses on two spans of data: one span starting in 1872, the other in 1957 ...

Let π be a partition. BG-rank(π) is defined as an alternating sum of parities of parts of π [1]. In [2], Berkovich and Garvan found theta series representations for the t-core generating functions P n≥0 at,j(n)q , where at,j(n) denotes the number of t-cores of n with BG-rank = j. In addition, they found positive eta-quotient representations for odd t-core generating functions with extreme value...

We present a dedicated algorithm for the nonnegative factorization of a correlation matrix from an application in financial engineering. We look for a low-rank approximation. The origin of the problem is discussed in some detail. Next to the description of the algorithm, we prove, by means of a counter example, that an exact nonnegative decomposition of a general positive semidefinite matrix is...

We introduce co-occurring directions sketching, a deterministic algorithm for approximate matrix product (AMM), in the streaming model. We show that co-occurring directions achieves a better error bound for AMM than other randomized and deterministic approaches for AMM. Co-occurring directions gives a (1 + ")-approximation of the optimal low rank approximation of a matrix product. Empirically o...

The classical two-sample problem is extended here to the case where the distribution functions of the observable random variables are specified functions of unknown distribution functions and the null hypothesis to be tested or the parameter to be estimated relates to these unknown distributions. Various properties of the proposed rank tests and derived estimates are studied.

Structured low-rank approximation is the problem of minimizing a weighted Frobenius distance to a given matrix among all matrices of fixed rank in a linear space of matrices. We study the critical points of this optimization problem using algebraic geometry. A particular focus lies on Hankel matrices, Sylvester matrices and generic linear spaces.