Under certain assumptions we show that a wavelet frame {τ(Aj , bj,k)ψ}j,k∈Z := {|detAj |−1/2ψ(A−1 j (x− bj,k))}j,k∈Z in L2(Rd) remains a frame when the dilation matrices Aj and the translation parameters bj,k are perturbed. As a special case of our result, we obtain that if {τ(Aj , ABn)ψ}j∈Z,n∈Zd is a frame for an expansive matrix A and an invertible matrix B, then {τ(Aj , ABλn)ψ}j∈Z,n∈Zd is a ...

Non-Hermitian Hamiltonians H 6= H possess the real (i.e., observable) spectra inside certain specific, “physical” domains of parameters D = D(H). In general, the determination of their “observability-horizon” boundaries ∂D is difficult. We list the pseudo-Hermitian real N by N matrix Hamiltonians for which the “prototype” horizons ∂D are defined by closed analytic formulae.

Low-rank matrix approximation has been widely adopted in machine learning applications with sparse data, such as recommender systems. However, the sparsity of the data, incomplete and noisy, introduces challenges to the algorithm stability – small changes in the training data may significantly change the models. As a result, existing low-rank matrix approximation solutions yield low generalizat...

The stability radius of a matrix polynomial P (λ) relative to an open region Ω of the complex plane and its relation to the numerical range of P (λ) are investigated. Using an expression of the stability radius in terms of λ on the boundary of Ω and ‖P (λ)−1‖2, a lower bound is obtained. This bound for the stability radius involves the distances of Ω to the connected components of the numerical...

Topic models can provide us with an insight into the underlying latent structure of a large corpus of documents. A range of methods have been proposed in the literature, including probabilistic topic models and techniques based on matrix factorization. However, in both cases, standard implementations rely on stochastic elements in their initialization phase, which can potentially lead to differ...

We propose a method of estimating the fast-scale stability margin of dc–dc converters based on Filippov’s theory—originally developed for mechanical systems with impacts and stick-slip motion. In this method one calculates the state transition matrix over a complete clock cycle, and the eigenvalues of this matrix indicate the stability margin. Important components of this matrix are the state t...

It is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive deniteness and stability of interval matricescan be presented. These conditions have been proved previously with variousmethods and now we provide some new proofs for them with a unity method.Furthermore we introduce a new necessary and sucient condition for checkingstability of interval...

It is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive deniteness and stability of interval matricescan be presented. These conditions have been proved previously with variousmethods and now we provide some new proofs for them with a unity method.Furthermore we introduce a new necessary and sucient condition for checkingstability of interval...

and Applied Analysis 3 whereW andZ are the solutions of (15) and (16), respectively, and I is the n × n identity matrix. Therefore, Φ(t, t 0 , x 0 ) = W(t, t 0 ) ⊗ Z T (t, t 0 ) . (22) (ii) Employing Lemma 2 and substituting forΦ the righthand side of (22), we get y (t, t 0 , x 0 ) = x (t, t 0 , x 0 )