A problem for many kernel-based methods is that the amount of computation required to find the solution scales as O(n3), where n is the number of training examples. We develop and analyze an algorithm to compute an easily-interpretable low-rank approximation to an n× n Gram matrix G such that computations of interest may be performed more rapidly. The approximation is of the form G̃k = CW + k C ...

We revisit a technique for solving multi-objective control problems through aanely parameterizing the closed-loop system with the Youla parameterization and conning the search of the Youla parameter to nite-dimensional subspaces. It is pretty well-known how to solve such problems if the closed-loop speciication are formulated in terms of the solvability of linear matrix inequalities. However, a...

We prove an adiabatic theorem for the evolution of spectral data under a weak additive perturbation in the context of a system without an intrinsic time scale. For continuous functions of the unperturbed Hamiltonian the convergence is in norm while for a larger class functions, including the spectral projections associated to embedded eigenvalues, the convergence is in the strong operator topol...

We consider the problem of variation of spectral subspaces for linear self-adjoint operators under off-diagonal perturbations. We prove a number of new optimal results on the shift of the spectrum and obtain (sharp) estimates on the norm of the difference of two spectral projections.

We prove an adiabatic theorem for the evolution of spectral data under a weak additive perturbation. For continuous functions of the unperturbed Hamiltonian the convergence is in norm while for a larger class functions, including the spectral projections associated to embedded eigenvalues, the convergence is in the strong operator topology.

introduction raman spectroscopy is a vibrational spectroscopic technique, based on inelastic scattering of monochromatic light. this technique can provide valuable information about biomolecular changes, associated with neoplastic transformation. the purpose of this study was to find raman spectral markers for distinguishing normal samples from cancerous ones in different tissues. materials and...

We show that given an estimate  that is close to a general high-rank positive semidefinite (PSD) matrix A in spectral norm (i.e., ‖Â−A‖2 ≤ δ), the simple truncated Singular Value Decomposition of  produces a multiplicative approximation of A in Frobenius norm. This observation leads to many interesting results on general high-rank matrix estimation problems: 1. High-rank matrix completion: we...

We obtain an explicit asymptotic formula for the norms of the spectral projections of the non-self-adjoint harmonic oscillator H. We deduce that the spectral expansion of e−Ht is norm convergent if and only if t is greater than a certain explicit positive constant.

For a given family of matrices F , we present a methodology to construct (complex) polytope Barabanov norms (and, when F is nonnegative, polytope Barabanov monotone norms and antinorms). Invariant Barabanov norms have been introduced by Barabanov and constitute an important instrument to analyze the joint spectral radius of a set of matrices. In particular, they played a key role in the disprov...

The generalized spectral radius, also known under the name of joint spectral radius, or (after taking logarithms) maximal Lyapunov exponent of a discrete inclusion is examined. We present a new proof for a result of Barabanov, which states that for irreducible sets of matrices an extremal norm always exists. This approach lends itself easily to the analysis of further properties of the generali...