A norm-preserving $H\sp \infty$ extension problem

Inapproximability Results for the Closest Vector Problem with Preprocessing over infty Norm

We show that the Closest Vector Problem with Preprocessing over `∞ norm (CVPP∞) is NP-hard to approximate to within a factor of (log n)1/2− , unless NP⊆ DTIME (2polylog(n)). The result is the same as that in [19] by Regev and Rosen, but our proof methods are different from theirs. Their reductions are based on norm embeddings. However, our reductions are based on the reduction of [2] and the pr...

Piecewise Convex-Concave Approximation in the $\ell_{\infty}$ Norm

Suppose that f ∈ IR is a vector of n error-contaminated measurements of n smooth values measured at distinct and strictly ascending abscissae. The following projective technique is proposed for obtaining a vector of smooth approximations to these values. Find y minimizing ‖y− f‖∞ subject to the constraints that the second order consecutive divided differences of the components of y change sign ...

Faster algorithms for SVP and CVP in the $\ell_{\infty}$ norm

Blomer and Naewe[BN09] modified the randomized sieving algorithm of Ajtai, Kumar and Sivakumar[AKS01] to solve the shortest vector problem (SVP). The algorithm starts with $N = 2^{O(n)}$ randomly chosen vectors in the lattice and employs a sieving procedure to iteratively obtain shorter vectors in the lattice. The running time of the sieving procedure is quadratic in $N$. We study this problem ...

The discrete-time $H_\infty$ control problem with measurement feedback

Ben M. Chen t Department of Electrical Engineering State University of New York a.t Stony Brook Stony Brook, NY 11794-2350 U.S.A. This paper is concerned with the discrete-time IIoo control problem with measurement feedback. We extend previous results by having weaker assumptions on the system parameters. We also show explicitly the structure of II00 controllers. Finally, we show that it is in ...

The ¿-norm Extension Property for Banach Spaces1