A Block-Sparse Tensor Train Format for Sample-Efficient High-Dimensional Polynomial Regression
Frontiers in Applied Mathematics and Statistics, 2021 Low-rank tensors are an established framework for the parametrization of multivariate polynomials. We propose to extend this framework by including the concept of block-sparsity to efficiently parametrize homogeneous, multivariate polynomials with low ...
Michael Götte +2 more
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Spectra of algebras of block-symmetric analytic functions of bounded type
Математичні Студії, 2022 We investigate algebras of block-symmetric analytic functions on spaces $\ell_{p}(\mathbb{C}^s)$ which are $\ell_{p}$-sums of $\mathbb{C}^{s}.$ We consider properties of algebraic bases of block-symmetric polynomials, intertwining operations on spectra ...
A. Zagorodnyuk, V. V. Kravtsiv
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Zeros of block-symmetric polynomials on Banach spaces
Математичні Студії, 2020 We investigate sets of zeros of block-symmetric polynomials on the direct sums of sequence spaces. Block-symmetric polynomials are more general objects than classical symmetric polynomials.
V. Kravtsiv
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Roots of Characteristic Polynomial Sequences in Iterative Block Cyclic Reductions
Mathematics, 2021 The block cyclic reduction method is a finite-step direct method used for solving linear systems with block tridiagonal coefficient matrices. It iteratively uses transformations to reduce the number of non-zero blocks in coefficient matrices.
Masato Shinjo +3 more
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Analogues of the Newton formulas for the block-symmetric polynomials on $\ell_p(\mathbb{C}^s)$
Karpatsʹkì Matematičnì Publìkacìï, 2020 The classical Newton formulas gives recurrent relations between algebraic bases of symmetric polynomials. They are true, of course, for symmetric polynomials on infinite-dimensional Banach sequence spaces.
V.V. Kravtsiv
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Parabolic Catalan numbers count flagged Schur functions and their appearances as type A Demazure characters (key polynomials) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 Fix an integer partition lambda that has no more than n parts. Let beta be a weakly increasing n-tuple with entries from {1,..,n}. The flagged Schur function indexed by lambda and beta is a polynomial generating function in x_1, .., x_n for certain ...
Robert A. Proctor, Matthew J. Willis
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Algebraic basis of the algebra of block-symmetric polynomials on $\ell_1 \oplus \ell_{\infty}$
Karpatsʹkì Matematičnì Publìkacìï, 2019 We consider so called block-symmetric polynomials on sequence spaces $\ell_1\oplus \ell_{\infty}, \ell_1\oplus c, \ell_1\oplus c_0,$ that is, polynomials which are symmetric with respect to permutations of elements of the sequences.
V.V. Kravtsiv
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Continuous block-symmetric polynomials of degree at most two on the space $(L_\infty)^2$
Karpatsʹkì Matematičnì Publìkacìï, 2016 We introduce block-symmetric polynomials on $(L_\infty)^2$ and prove that every continuous block-symmetric polynomial of degree at most two on $(L_\infty)^2$ can be uniquely represented by some "elementary" block-symmetric polynomials.
T.V. Vasylyshyn
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ON GENERALIZATIONS OF THE HILBERT NULLSTELLENSATZ FOR INFINITY DIMENSIONS (A SURVEY)
Journal of Vasyl Stefanyk Precarpathian National University, 2015 The paper contains a proof of Hilbert Nullstellensatz for the polynomials oninfinite-dimensional complex spaces and for a symmetric and a block-symmetric polynomials.
V.V. Kravtsiv
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Representation of spectra of algebras of block-symmetric analytic functions of bounded type
Karpatsʹkì Matematičnì Publìkacìï, 2016 The paper contains a description of symmetric convolution of the algebra of block-symmetric analytic functions of bounded type on $\ell_{1}$-sum of the space $\mathbb{C}^{2}.$ We show that the specrum of such algebra does not coincide of point evaluation
V.V. Kravtsiv, A.V. Zagorodnyuk
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