Symmetric functions and the Vandermonde matrix
Open accessThe claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
The Art of Computer Programming
Knuth, D. E. (1968) · Cited by 16,097 · see citing works
Symmetric Functions and Hall Polynomials
MacDonald, I. G. (1995) · doi:10.1093/oso/9780198534891.001.0001 · Cited by 7,797 · see citing works
Stanley, R. P., & Rota, G. (1997) · Cambridge University Press eBooks · doi:10.1017/cbo9780511805967 · Cited by 6,407 · see citing works
Andrews, G. E. (1984) · Cambridge University Press eBooks · doi:10.1017/cbo9780511608650 · Cited by 3,124 · see citing works
Spline Functions: Basic Theory.
Smith, P. W., & Schumaker, L. L. (1982) · Mathematics of Computation · doi:10.2307/2007301 · Cited by 2,499 · see citing works
Stanley, R. P., & Fomin, S. (1999) · Cambridge University Press eBooks · doi:10.1017/cbo9780511609589 · Cited by 2,203 · see citing works
SPLINE FUNCTIONS: Basic Theory
Churchhouse, R. F. (1982) · Bulletin of the London Mathematical Society · doi:10.1112/blms/14.2.175 · Cited by 549 · see citing works
Interpolation and Approximation by Polynomials
Phillips, G. M. (2003) · CMS books in mathematics · doi:10.1007/b97417 · Cited by 486 · see citing works
Interpolation and approximation by polynomials
Phillips, G. M. (. M. (2004) · Choice Reviews Online · doi:10.5860/choice.41-5959 · Cited by 438 · see citing works
Solution of Vandermonde systems of equations
Björck, Ȧ., & Pereyra, V. (1970) · Mathematics of Computation · doi:10.1090/s0025-5718-1970-0290541-1 · Cited by 398 · see citing works
Solution of Vandermonde Systems of Equations
Björck, Å., & Pereyra, V. L. (1970) · Mathematics of Computation · doi:10.2307/2004623 · Cited by 248 · see citing works
Total Positivity and Its Applications
Gasca, M., & Micchelli, C. A. (1996) · Springer eBooks · doi:10.1007/978-94-015-8674-0 · Cited by 246 · see citing works
The q-Stirling numbers of first and second kinds
Gould, H. W. (1961) · Duke Mathematical Journal · doi:10.1215/s0012-7094-61-02826-5 · Cited by 152 · see citing works
q-Bernstein polynomials and Bézier curves
Oruç, H., & Phillips, G. M. (2002) · Journal of Computational and Applied Mathematics · doi:10.1016/s0377-0427(02)00733-1 · Cited by 111 · see citing works
Self-citationThe linear algebra of the generalized Pascal matrix
Zhang, Z. (1997) · Linear Algebra and its Applications · doi:10.1016/0024-3795(95)00452-1 · Cited by 92 · see citing works
Stirling matrix via Pascal matrix
Cheon, G., & Kim, J. (2001) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(01)00234-8 · Cited by 65 · see citing works
Explicit factorization of the Vandermonde matrix
Oruç, H., & Phillips, G. M. (2000) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(00)00124-5 · Cited by 57 · see citing works
Self-citationConvexity and generalized Bernstein polynomials
Goodman, T. N. T., Oruç, H., & Phillips, G. M. (1999) · Proceedings of the Edinburgh Mathematical Society · doi:10.1017/s0013091500020101 · Cited by 56 · see citing works
Self-citationThe Fast Generalized Parker–Traub Algorithm for Inversion of Vandermonde and Related Matrices
Gohberg, I., & Olshevsky, V. (1997) · Journal of Complexity · doi:10.1006/jcom.1997.0442 · Cited by 51 · see citing works
On the Convergence and Iterates of q-Bernstein Polynomials
Oruç, H., & Tuncer, N. (2002) · Journal of Approximation Theory · doi:10.1006/jath.2002.3703 · Cited by 49 · see citing works
Self-citationFactorizations of Cauchy-Vandermonde matrices
Martínez, J., & Peña, J. M. (1998) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(98)10073-3 · Cited by 39 · see citing works
Fast algorithms of Björck-Pereyra type for solving Cauchy-Vandermonde linear systems
Martínez, J., & Peña, J. M. (1998) · Applied Numerical Mathematics · doi:10.1016/s0168-9274(97)00102-5 · Cited by 26 · see citing works
Generalized Binomial Coefficients and the Subset–Subspace Problem
Konvalina, J. (1998) · Advances in Applied Mathematics · doi:10.1006/aama.1998.0598 · Cited by 23 · see citing works
Triangular factors of Cauchy and Vandermonde matrices
Gohberg, I., & Koltracht, I. (1996) · Integral Equations and Operator Theory · doi:10.1007/bf01229504 · Cited by 17 · see citing works
Vandermonde matrices on integer nodes
Eisinberg, A., Franzè, G., & Pugliese, P. (1998) · Numerische Mathematik · doi:10.1007/s002110050360 · Cited by 16 · see citing works
Vandermonde matrices on integer nodes: the rectangular case
Eisinberg, A., Pugliese, P., & Salerno, N. (2001) · Numerische Mathematik · doi:10.1007/pl00005428 · Cited by 12 · see citing works
Generalized Bernstein polynomials and total positivity
Oruç, H. (1999) · St Andrews Research Repository (St Andrews Research Repository) · Cited by 8 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 1
- G.M. Phillips, Two Millenia of Mathematics from Archimedes to Gauss, Springer, New York, 2000.
Cited by
Sorted by citations
Perera, S. M., Ariyarathna, V., Udayanga, N., Madanayake, A., Wu, G., Belostotski, L., Wang, Y., Mandal, S., Cintra, R. J., & Rappaport, T. S. (2018) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2018.2822940 · Cited by 50 · see citing works
Perera, S. M., Madanayake, A., & Cintra, R. J. (2020) · IEEE Access · doi:10.1109/access.2020.2970342 · Cited by 18 · see citing works
Efficient and Self-Recursive Delay Vandermonde Algorithm for Multi-beam Antenna Arrays
Perera, S. M., Madanayake, A., & Cintra, R. J. (2020) · IEEE Open Journal of Signal Processing · doi:10.1109/ojsp.2020.2991586 · Cited by 15 · see citing works
A Fast DVM Algorithm for Wideband Time-Delay Multi-Beam Beamformers
Perera, S. M., Lingsch, L., Madanayake, A., Mandal, S., & Mastronardi, N. (2022) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2022.3231182 · Cited by 11 · see citing works
Thiran Filters for Wideband DSP-Based Multi-Beam True Time Delay RF Sensing Applications
Perera, S. M., Rathnasekara, G., & Madanayake, A. (2024) · Sensors · doi:10.3390/s24020576 · Cited by 5 · see citing works
- Authors
- Oruç, H., & Akmaz, H. K.
- Affiliations
- Dokuz Eylül University (TR)
- Corresponding author
- Oruç, Halil
- ORCID
- Oruç, Halil
- Venue
- Journal of Computational and Applied Mathematics
- Publisher
- Elsevier BV
- Published
- 2004-11
- Volume
- 172
- Issue
- 1
- Pages
- 49-64
- ISSN
- 0377-0427 (ISSN-L)
- OpenAlex
- W2156010507
- Cited by
- 25
- References
- 27
- Citations by year
- 2024: 1 · 2022: 3 · 2021: 3 · 2020: 3 · 2019: 2 · 2018: 1 · 2016: 2 · 2015: 1 · 2012: 1
- FWCI
- 2.37
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Journal of Computational and Applied Mathematics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical functions and polynomials
- Keywords
- Vandermonde matrix, matrix inverse, symmetric functions, combinatorial identities, q-binomial coefficients, q-Stirling numbers, Pascal matrix, recursive computation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
