相关论文: Decay bounds for functions of matrices with banded…
For many functions of matrices $f(A)$, it is known that their entries exhibit a rapid -- often exponential or even superexponential -- decay away from the sparsity pattern of the matrix $A$. In this paper we specifically focus on the class…
Bounds on the exponential decay of generalized eigenfunctions of bounded and unbounded selfadjoint Jacobi matrices are established. Two cases are considered separately: (i) the case in which the spectral parameter lies in a general gap of…
Given matrices $A$ and $B$ such that $B=f(A)$, where $f(z)$ is a holomorphic function, we analyze the relation between the singular values of the off-diagonal submatrices of $A$ and $B$. We provide family of bounds which depend on the…
New bounds are derived for the eigenvalues of sums of Kronecker products of square matrices by relating the corresponding matrix expressions to the covariance structure of suitable bi-linear stochastic systems in discrete and continuous…
We develop new, easily computable exponential decay bounds for inverses of banded matrices, based on the quasiseparable representation of Green matrices. The bounds rely on a diagonal dominance hypothesis and do not require explicit…
Combined perturbation bounds are presented for eigenvalues and eigenspaces of Hermitian matrices or singular values and singular subspaces of general matrices. The bounds are derived based on the smooth decompositions and elementary…
Over the real numbers, the Kronecker sum is the unique operation on matrices which exponentiates to the Kronecker product. Kronecker quotients provide an algebraic view of decompositions of matrices in terms of Kronecker products. This…
Consider a matrix function f defined for Hermitian matrices. The purpose of this paper is two-fold. We derive new results for the absolute structured condition number of the matrix function and we derive new bounds for the perturbation…
In the present note, we study a new method of constructing efficient coverings for Kronecker powers of matrices, recently proposed by J. Alman, Y. Guan, A. Padaki [arXiv, 2022]. We provide an alternative proof for the case of symmetric…
The rigidity of a matrix $A$ for target rank $r$ is the minimum number of entries of $A$ that need to be changed in order to obtain a matrix of rank at most $r$. At MFCS'77, Valiant introduced matrix rigidity as a tool to prove circuit…
We show that in $\text{O}(D)$ invariant matrix theories containing a large number $D$ of complex or Hermitian matrices, one can define a $D\rightarrow\infty$ limit for which the sum over planar diagrams truncates to a tractable, yet…
We present a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. Our approach, based on commutator methods, applies to nets of unitary operators, unitary representations of topological…
I briefly review some recent progress in the theory of nonleptonic B decays. After introducing the operator product expansion and the relevant effective Hamiltonian, I discuss the domain of validity and the theoretical justification of the…
The existence of a smooth, nonnegative, compactly supported function with monotone (on the half-line) Fourier transform satisfying two-sided decay bounds is demonstrated.
A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…
Networks are frequently studied algebraically through matrices. In this work, we show that networks may be studied in a more abstract level using results from the theory of matroids by establishing connections to networks by decomposition…
We present two companion results: Phragm\'en-Lindel\"of type tight bounds on the minimal possible growth of subharmonic functions with recurrent zero set, and tight bounds on the maximal possible decay of the harmonic measure of the outer…
This work is concerned with variational analysis of so-called spectral functions and spectral sets of matrices that only depend on eigenvalues of the matrix. Based on our previous work [H. T. B\`ui, M. N. B\`ui, and C. Clason, Convex…
We derive a uniform bound for the difference of two contractive semigroups, if the difference of their generators is form-bounded by the Hermitian parts of the generators themselves. We construct a semigroup dynamics for second order…
In the present paper continuing our previous work we prove an extension theorem for matrices with entries in the algebra of bounded holomorphic functions defined on an unbranched covering of a Caratheodory hyperbolic Riemann surface of…