Sergei Friedland

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We consider the formulation and local analysis of various quadratically convergent methods for solving the symmetric matrix inverse eigenvalue problem. One of these methods is new. We study the case where multiple eigenvalues are given: we show how to state the problem so that it is not overdetermined, and describe how to modify the numerical methods to(More)
We extend the multiplicative submodularity of the principal determinants of a nonnegative definite hermitian matrix to other spectral functions. We show that if f is the primitive of a function that is operator monotone on an interval containing the spectrum of a hermitian matrix A, then the function I 7→ trf(A[I]) is supermodular, meaning that(More)
In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given tensor by a tensor that is sparsely representable. For matrices, i.e. 2-tensors, such a representation can be obtained via the singular value decomposition which allows to compute the best rank k approximations. For t-tensors with t > 2(More)
Let A be an infinite sign regular (sr) matrix which can be viewed as a bounded linear operator from lO to itself. It is proved here that if the range of A contains the sequence (..., 1,1,,-1,...), then A is onto. If A-l exists, then DA-1D is also sr, where D is the diagonal matrix with diagonal entries alternately I and -1. In case A is totally positive(More)
In this paper, we consider an extension and rigorous justification of Karhunen-Loeve transform (KLT) which is an optimal technique for data compression. We propose and study the generic KLT which is treated as the best weighted linear estimator of a given rank under the condition that the associated covariance matrix is singular. As a result, the generic(More)
The notion of a 1-vertex transfer matrix for multi-dimensional codes is introduced. It is shown that the capacity of such codes, or the topological entropy, can be expressed as the limit of the logarithm of spectral radii of 1-vertex transfer matrices. Storage and computations using the 1-vertex transfer matrix are much smaller than storage and computations(More)