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- Sergei Friedland, J . NOCEDAL, Michael L. Overton
- 1987

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)

- Sergei Friedland
- 2007

In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given m × n matrix A by a matrix B of rank at most k which is much smaller than m and n. The best rank k approximation can be determined via the singular value decomposition which, however, has prohibitively high computational complexity and… (More)

x0. Introduction Let X be a compact metric space and assume that f : X ! X is a continuous map. Denote by the nonwandering set of f. An interesting and a nontrivial invariant of f is HD(()-the Hausdorr dimension of. It is usually a highly nontrivial problem to nd HD((). The seminal work of Bowen Bow2] gives HD(() as the solution to P(tt) = 0 for some… (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)

- Sergei Friedland, Stéphane Gaubert
- ArXiv
- 2010

In this paper we prove an analog of Perron-Frobenius theorem for multilinear forms with nonnegative coefficients. 2000 Mathematics Subject Classification. 15A48, 47H07, 47H09, 47H10.

- Author C. de Boor, Sergei Friedland, Allan Pinkus, Allan Pinkus
- 1980

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)

- Anatoli Torokhti, Sergei Friedland, Phil G. Howlett
- 2007 IEEE International Symposium on Information…
- 2007

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)