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(14 citation statements)

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“…(a) It was proved in Theorem 3.1 (ii) of [3]. (b) All entries of the k-th column of the matrix L q have as common factor n k−1 q (k−1)(k−2)/2 and all the entries of the l-th row have as common factor 1/ n k=2 (1…”

confidence: 99%

“…(a) It was proved in Theorem 3.1 (ii) of [3]. (b) All entries of the k-th column of the matrix L q have as common factor n k−1 q (k−1)(k−2)/2 and all the entries of the l-th row have as common factor 1/ n k=2 (1…”

confidence: 99%

“…In this paper we shall prove that we can perform with Lupaş matrices many algebraic computations with high relative accuracy, including the computation of their inverses, their eigenvalues or their singular values. Up to now, such computations with high relative accuracy are possible with only a few classes of matrices, such as Vandermonde matrices and their generalizations [6], Bernstein-Vandermonde matrices [17], Said-Ball matrices [18], rational collocation matrices [3] or Jacobi-Stirling matrices [4]. where a n i,q (t) = n i q i(i−1)…”

confidence: 99%

“…This has been achieved in some important subclasses of TP matrices with applications to computer-aided geometric design (cf. other works 2,3,9,10 ), finance (cf. the work of Delgado et al 11 ), or combinatorics (cf.…”

confidence: 99%

“…Demmel). Among the classes of matrices for which algorithms to HRA have been constructed, we can mention some subclasses of nonsingular totally positive (TP) matrices . As shown in Koev, for a nonsingular TP matrix A , the adequate parameterization to obtain computations to HRA is its bidiagonal factorization $\mathrm{scriptB}\mathrm{scriptD}\left(A\right)$.…”

confidence: 99%

“…Among the classes of matrices for which algorithms to HRA have been constructed, we can mention some subclasses of nonsingular totally positive (TP) matrices. [13][14][15][16] As shown in Koev, 17,18 for a nonsingular TP matrix A, the adequate parameterization to obtain computations to HRA is its bidiagonal factorization (A). Given a matrix A = (a ij ) 1 ≤ i, j ≤ n , the conversion matrix of A is the matrix A # : = (a n + 1 − i, n + 1 − j ) 1 ≤ i, j ≤ n .…”

confidence: 99%