Inverses of Vandermonde matrices
Integrity signals
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“, [21, 25]).”
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“sing bounded (e.g., double) precision of computing rules out using the cited fast algorithms, and the known double precision algorithms for Problems 1{4 require quadratic arithmetic time (cf. [BF00], [P64], [BP70], [BEGO08]). This pessimistic outcome, however, does not apply to the important special case where the kno…”
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“Table 1 Fast O(n2) algorithms for three-term Vandermonde matrices Coefficient matrix Inversion algorithm Algorithm solving linear system Vandermonde Parker–Forney–Traub algorithm [28,10,32] Björck–Pereyra algorithm [6] Chebyshev–Vandermonde Gohberg–Olshevsky algorithm [15] Reichel-Opfer algorithm [31] Three-term Vande…”
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“…problems, such as computing the inverse of a Vandermonde matrix (resulting in inversion formulas or inversion algorithms) or solving systems of equations with a Vandermonde matrix as the coefficient matrix [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], are not considered in this paper.”
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INTERTEMPORAL COMPLEMENTARITY AND OPTIMALITY: A STUDY OF A TWO‐DIMENSIONAL DYNAMICAL SYSTEM*
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“For one such approach, see Parker (1964).”
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“Since this is a Vandermonde matrix, the system in (2) can be solved in 6 k 2 arithmetic operations [32], [33].”
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“The key idea [7] is to replace the inner product of a vector b = ( b0, b1, b2, .”
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Fast Inversion of Vandermonde and Vandermonde-Like Matrices
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A Fast Algorithm for the Inversion of Quasiseparable Vandermonde-like MatricesPreprint
Perera, S. M., Bonik, G., & Olshevsky, V. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1401.1874
“[7, 6, 24, 14, 10, 25, 28]) were derived by using the properties of so called associate or Horner polynomials.”
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Codes correcting phased burst erasures
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“The length of the codes is n = (E), where”
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The Sparse Hausdorff Moment Problem, with Application to Topic ModelsPreprint
Gordon, S., Mazaheri, B., Schulman, L. J., et al. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2007.08101
“, O(k2) arithmetic operations, for instance using Parker’s algorithm [22]; by Lemma 30 the procedure RECTIFYWEIGHTS takes O(k) operations).”
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A conjecture of Coleman on the Eisenstein family
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- Authors
- Parker, F. D.
- Corresponding author
- Parker, F. D.
- Venue
- The American Mathematical Monthly
- Publisher
- JSTOR
- Published
- 1964-04
- Volume
- 71
- Issue
- 4
- Pages
- 410
- ISSN
- 0002-9890 (ISSN-L)
- OpenAlex
- W2332687951
- Cited by
- 35
- References
- 0
- Citations by year
- 2024: 2 · 2023: 1 · 2022: 1 · 2020: 1 · 2019: 1 · 2016: 1 · 2015: 1 · 2014: 3 · 2013: 3
- FWCI
- 0.51
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- American Mathematical Monthly (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical functions and polynomials
- Keywords
- Vandermonde matrix, matrix inverse, polynomial interpolation, linear systems
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