A Björck-Pereyra-type algorithm for Szegö-Vandermonde matrices based on properties of unitary Hessenberg matrices
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Cites
Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505 · see citing works
The Commutant Lifting Approach to Interpolation Problems
Foiaş, C., & Frazho, A. E. (1990) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-7712-1 · Cited by 604 · see citing works
Adaptive IIR Filtering in Signal Processing and Control
Regalia, P. A. (2018) · Routledge eBooks · doi:10.1201/9781315136653 · Cited by 420 · 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
Polynomials orthogonal on a circle and their applications
Геронимус, Я. Л. (1954) · American Mathematical Society eBooks · Cited by 248 · 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
Tyrtyshnikov, E. E. (1994) · Numerische Mathematik · doi:10.1007/s002110050027 · Cited by 142 · see citing works
Newton interpolation at Leja points
Reichel, L. (1990) · BIT Numerical Mathematics · doi:10.1007/bf02017352 · Cited by 129 · see citing works
The QR algorithm for unitary Hessenberg matrices
Gragg, W. B. (1986) · Journal of Computational and Applied Mathematics · doi:10.1016/0377-0427(86)90169-x · Cited by 129 · see citing works
Gragg, W. B. (1993) · Journal of Computational and Applied Mathematics · doi:10.1016/0377-0427(93)90294-l · Cited by 125 · see citing works
Error analysis of the Bj�rck-Pereyra algorithms for solving Vandermonde systems
Higham, N. J. (1987) · Numerische Mathematik · doi:10.1007/bf01408579 · Cited by 89 · see citing works
Effectively Well-Conditioned Linear Systems
Chan, T. F.-C., & Foulser, D. E. (1988) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0909067 · Cited by 82 · see citing works
Schur's Algorithm and Several Applications
Bakonyi, M., & Constantinescu, T. (1992) · Cited by 79 · see citing works
Stability Analysis of Algorithms for Solving Confluent Vandermonde-Like Systems
Higham, N. J. (1990) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/0611002 · Cited by 77 · see citing works
Associated Polynomials and Uniform Methods for the Solution of Linear Problems
Traub, J. F. (1966) · SIAM Review · doi:10.1137/1008061 · Cited by 76 · see citing works
A divide and conquer method for unitary and orthogonal eigenproblems
Gragg, W. B., & Reichel, L. (1990) · Numerische Mathematik · doi:10.1007/bf01386438 · Cited by 66 · see citing works
Fast Algorithms for Structured Matrices: Theory and Applications
Olshevsky, V. (2003) · Contemporary mathematics - American Mathematical Society · doi:10.1090/conm/323 · Cited by 65 · see citing works
Self-citationReichel, L., & Opfer, G. (1991) · Mathematics of Computation · doi:10.1090/s0025-5718-1991-1094957-9 · Cited by 55 · see citing works
Prediction Theory and Harmonic Analysis.
Whittle, P. J. L., Mandrekar, V. S., & Salehi, H. (1984) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2981610 · Cited by 54 · see citing works
Displacement structure approach to polynomial Vandermonde and related matrices
Kailath, T., & Olshevsky, V. (1997) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(96)00315-1 · Cited by 50 · see citing works
Self-citationFast inversion of Chebyshev--Vandermonde matrices
Gohberg, I., & Olshevsky, V. (1994) · Numerische Mathematik · doi:10.1007/s002110050018 · Cited by 47 · see citing works
Self-citationFast inversion of vandermonde-like matrices involving orthogonal polynomials
Calvetti, D., & Reichel, L. (1993) · BIT Numerical Mathematics · doi:10.1007/bf01990529 · Cited by 46 · see citing works
A fast parallel Björck–Pereyra-type algorithm for solving Cauchy linear equations
Boros, T., Kailath, T., & Olshevsky, V. (1999) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(99)00115-9 · Cited by 39 · see citing works
Self-citationInverses of Vandermonde matrices
Parker, F. D. (1964) · The American Mathematical Monthly · doi:10.2307/2313246 · Cited by 35 · cited 1× · see citing works
“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…”
MethodGeneralized Schwarz form and lattice - ladder realizations of digital filters
Kimura, H. (1985) · IEEE Transactions on Circuits and Systems · doi:10.1109/tcs.1985.1085647 · Cited by 33 · see citing works
Structured matrices: recent developments in theory and computation
Bini, D. A., Tyrtyshnikov, E. E., & Yalamov, P. Y. (2001) · Cited by 22 · see citing works
Olshevsky, V. (1998) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(98)10099-x · Cited by 18 · see citing works
Self-citationPrediction theory and harmonic analysis : the Pesi Masani volume
Masani, P. R., Mandrekar, V. S., & Salehi, H. (1983) · Elsevier eBooks · Cited by 17 · see citing works
Continuation methods for the computation of zeros of Szegö polynomials
Ammar, G. S., Calvetti, D., & Reichel, L. (1996) · Linear Algebra and its Applications · doi:10.1016/0024-3795(95)00324-x · Cited by 16 · see citing works
Pivoting and backward stability of fast algorithms for solving Cauchy linear equations
Boros, T., Kailath, T., & Olshevsky, V. (2002) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(01)00519-5 · Cited by 15 · see citing works
Self-citationState-space structures of ladder canonical forms
Morf, M., & Lee, D. L. (1980) · IEEE Conference on Decision and Control including the Symposium on Adaptive Processes (CDC) · doi:10.1109/cdc.1980.271997 · Cited by 14 · see citing works
Pivoting for structured matrices and rational tangential interpolation
Olshevsky, V. (2003) · Contemporary mathematics - American Mathematical Society · doi:10.1090/conm/323/05696 · Cited by 11 · see citing works
Self-citationAn analogue for Szegő polynomials of the Clenshaw algorithm
Ammar, G. S., Gragg, W. B., & Reichel, L. (1993) · Journal of Computational and Applied Mathematics · doi:10.1016/0377-0427(93)90296-n · Cited by 7 · see citing works
誕生・プログラミングデザイナ- (特集 いまどき熟れごろ「ビジュアル言語」どれが買いか)
武山, 良. (1998) · BIT Numerical Mathematics · Cited by 4 · see citing works
Flagged first, then by citations
Research works printed but not linked: 3
- G. Forney, Concatenated Codes, The MIT Press, Cambridge, 1966.
- U. Grenader, G. Szegö, Toeplitz Forms and Applications, University of California Press, 1958.
- M. Takizawa, Hisao Kishi, N. Hamada, Synthesis of lattice digital filter by the state space variable method, Trans. IECE Jpn. J65-A (1983) 363-370.
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Bella, T., Eidelman, Y., Gohberg, I., Koltracht, I., & Olshevsky, V. (2009) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/060676635 · Cited by 14 · see citing works
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Perera, S. M., Rathnasekara, G., & Madanayake, A. (2024) · Sensors · doi:10.3390/s24020576 · Cited by 5 · see citing works
A Fast Algorithm to Solve Delay Vandermonde Systems in Phased-Array Digital Receivers
Perera, S. M., Madanayake, A., Ogle, A., Silverio, D., & Huang, J. Q. (2021) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2021.3086356 · Cited by 5 · see citing works
- Authors
- Bella, T., Eidelman, Y., Gohberg, I., Koltracht, I., & Olshevsky, V.
- Affiliations
- University of Connecticut (US)
- Tel Aviv University (IL)
- Corresponding author
- Bella, Tom
- Venue
- Linear Algebra and its Applications
- Publisher
- Elsevier BV
- Published
- 2007-01
- Volume
- 420
- Issue
- 2-3
- Pages
- 634-647
- ISSN
- 0024-3795 (ISSN-L)
- OpenAlex
- W2078755977
- Cited by
- 17
- References
- 34
- Citations by year
- 2024: 2 · 2023: 2 · 2022: 1 · 2021: 2 · 2018: 1 · 2013: 3 · 2012: 1
- FWCI
- 0.70
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Linear Algebra and its Applications (publishedVersion)
- Funders
- National Science Foundation (0242518)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical functions and polynomials
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Polynomial and algebraic computation
- Keywords
- Szegő polynomials, ill-conditioned matrices
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