Reenement equations play an important role in computer graphics and wavelet analysis. In this paper we investigate multivariate reenement equations associated with a dila-tion matrix and a nitely supported reenement mask. We characterize the L p-convergence of a subdivision scheme in terms of the p-norm joint spectral radius of a collection of matrices associated with the reenement mask. In par...

Positive definite matrix approximation with a condition number constraint is an optimization problem to find the nearest positive definite matrix whose condition number is smaller than a given constant. We demonstrate that this problem can be converted to a simpler one in this note when we use a unitary similarity invariant norm as a metric. We can especially convert it to a univariate piecewis...

In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix. Taking an approach different from existing literature, our method first involves a specific biased sampling, with an element being chosen based on the leverage scores of its row and column, and then involves weighted alternating minimization over the factored form of the intended low-ra...

In this paper, we obtain the spectral norm and eigenvalues of circulant matrices with Horadam’s numbers. Furthermore, we define the semicirculant matrix with these numbers and give the Euclidean norm of this matrix. 2000 Mathematics Subject Classification: 11B39; 15A36; 15A60; 15A18.

Some new perturbation bounds of the positive (semi) definite polar factor and the (sub) unitary polar factor for the (generalized) polar decomposition under the general unitarily invariant norm and the spectral norm are presented. By applying our new bounds to the weighted cases, the known perturbation bounds for the weighted polar decomposition are improved. 2014 Elsevier Inc. All rights reser...

We present an efficient spectral projected-gradient algorithm for optimization subject to a group `1-norm constraint. Our approach is based on a novel linear-time algorithm for Euclidean projection onto the `1and group `1-norm constraints. Numerical experiments on large data sets suggest that the proposed method is substantially more efficient and scalable than existing methods.

The spectral radius of every d× d matrix A is bounded from below by c ‖A‖ ‖A‖, where c = c(d) > 0 is a constant and ‖·‖ is any operator norm. We prove an inequality that generalizes this elementary fact and involves an arbitrary number of matrices. In the proof we use geometric invariant theory. The generalized spectral radius theorem of Berger and Wang is an immediate consequence of our inequa...

The efficiency of many speech processing methods rely on accurate modeling of the distribution of the signal spectrum and a majority of prior works suggest that the spectral components follow the Laplace distribution. To improve the probability distribution models based on our knowledge of speech source modeling, we argue that the model should in fact be a multiplicative mixture model, includin...

A class of numerical methods is developed for second order Volterra integrodifferential equations by using a Legendre spectral approach. We provide a rigorous error analysis for the proposed methods, which shows that the numerical errors decay exponentially in the L∞-norm and L-norm. Numerical examples illustrate the convergence and effectiveness of the numerical methods. AMS subject classifica...

We prove that a composition operator is bounded on the Hardy space H of the right half-plane if and only if the inducing map fixes the point at infinity non-tangentially, and has a finite angular derivative λ there. In this case the norm, essential norm, and spectral radius of the operator are all equal to √ λ.