Usually when singular values are clustered the eigenvalues behave similarly However it is not the case if we make no assumptions Here we present examples when the singular values are clusteredâ€¦ (More)

We show that the recent tensor-train (TT) decompositions of matrices come up from its recursive Kronecker-product representations with a systematic use of common bases. The names TTM and QTT used inâ€¦ (More)

We consider two problems related to polar codes. First is the problem of polar codes construction and analysis of their performance without Monte-Carlo method. The formulas proposed are the same asâ€¦ (More)

Abstract. We consider halfâ€“infinite triangular Toeplitz matrices with slow decay of the elements and prove under a monotonicity condition that the elements of the inverse matrix, as well as theâ€¦ (More)

A new family of codes based on polar codes, soft concatenation and list+CRC decoding is proposed. Numerical experiments show the performance competitive with industry standards and Tal, Vardyâ€¦ (More)