Look-ahead Levinson- and Schur-type recurrences in the Padé table.
Low rank co-diagonal matrices and Ramsey graphs.
Low rank Tucker-type tensor approximation to classical potentials
This paper investigates best rank-(r 1,..., r d) Tucker tensor approximation of higher-order tensors arising from the discretization of linear operators and functions in ℝd. Super-convergence of the best rank-(r 1,..., r d) Tucker-type decomposition with respect to the relative Frobenius norm is proven. Dimensionality reduction by the two-level Tucker-to-canonical approximation is discussed. Tensor-product representation of basic multi-linear algebra operations is considered, including inner, outer...
Lower bounds for some factorable matrices.
Lower Bounds for the Condition Number of Vandermonde Matrices.
Lower bounds for the largest eigenvalue of the gcd matrix on
Consider the matrix with ’th entry . Its largest eigenvalue and sum of entries satisfy . Because cannot be expressed algebraically as a function of , we underestimate it in several ways. In examples, we compare the bounds so obtained with one another and with a bound from S. Hong, R. Loewy (2004). We also conjecture that for all . If is large enough, this follows from F. Balatoni (1969).
Lower bounds for the spectral norm.
Lower order terms for the one-level densities of symmetric power L-functions in the level aspect
Low-rank iterative methods for projected generalized Lyapunov equations.
Low-rank tensor representation of Slater-type and Hydrogen-like orbitals
The paper focuses on a low-rank tensor structured representation of Slater-type and Hydrogen-like orbital basis functions that can be used in electronic structure calculations. Standard packages use the Gaussian-type basis functions which allow us to analytically evaluate the necessary integrals. Slater-type and Hydrogen-like orbital functions are physically more appropriate, but they are not analytically integrable. A numerical integration is too expensive when using the standard discretization...
LU Decompositions of Generalized Diagonally Dominant Matrices
M-matrices: a generalization of M-matrices based on eventually nonnegative matrices.
-point invariants of real geometries.
Magnifying elements of transformation semigroups.
Majorants of matrix norms and spectrum localization
Majorization bounds for Ritz values of Hermitian matrices.
m-applications over finite fields
Maps on matrices that preserve the spectral radius distance
Let ϕ be a surjective map on the space of n×n complex matrices such that r(ϕ(A)-ϕ(B))=r(A-B) for all A,B, where r(X) is the spectral radius of X. We show that ϕ must be a composition of five types of maps: translation, multiplication by a scalar of modulus one, complex conjugation, taking transpose and (simultaneous) similarity. In particular, ϕ is real linear up to a translation.
Maps on upper triangular matrices preserving zero products
Consider —the ring of all upper triangular matrices defined over some field . A map is called a zero product preserver on in both directions if for all the condition is satisfied if and only if . In the present paper such maps are investigated. The full description of bijective zero product preservers is given. Namely, on the set of the matrices that are invertible, the map may act in any bijective way, whereas for the zero divisors and zero matrix one can write as a composition...
Maps preserving spectral radius, numerical radius, spectral norm.