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Items 101–200 of 202
A Superfast Randomized Algorithm to Decompose Binary Forms
Bender, M. R., Faugère, J., Perret, L., et al. (2016) · doi:10.1145/2930889.2930896 · Cited by 5
An Improved Computationally Efficient Method for Finding the Drazin Inverse
Jebreen, H. B., & Chalco-Cano, Y. (2018) · Discrete Dynamics in Nature and Society · doi:10.1155/2018/6758302 · Cited by 5
Quasi-optimal multiplication of linear differential operators
Benoit, A., Bostan, A., van der Hoeven, J., & Hoeven, V. D. (2012) · Cited by 7
Aperture Synthesis With Digital Array Radars and Covariant Change of Wavenumber Variables
Barnes, C. F. (2022) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2022.3221664 · Cited by 5
Inverting bijective polynomial maps over finite fields
Cafure, A., Matera, G., & Waissbein, A. (2006) · IEEE Information Theory Workshop (ITW) · doi:10.1109/itw.2006.1633775 · Cited by 5
“[26], [29]).”
Acceleration of Subdivision Root-Finding for Sparse Polynomials
Pan, V. Y. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-60026-6_27 · Cited by 6
Self-citationJet functions having indefinite Carathéodory–Pick matrices
Bolotnikov, V., Kheifets, A., & Rodman, L. (2003) · Linear Algebra and its Applications · doi:10.1016/j.laa.2003.09.006 · Cited by 5
Algorithmes rapides pour les polynômes, séries formelles et matrices
Bostan, A. (2010) · Les cours du CIRM · doi:10.5802/ccirm.9 · Cited by 5
On the Construction of a Two-Step Sixth-Order Scheme to Find the Drazin Generalized Inverse
Zhang, K., Soleymani, F., & Shateyi, S. (2024) · Axioms · doi:10.3390/axioms14010022 · Cited by 4
Real polynomial root-finding by means of matrix and polynomial iterations
Pan, V. Y., & Zhao, L. (2017) · Theoretical Computer Science · doi:10.1016/j.tcs.2017.03.032 · Cited by 4
Self-citationAdvancing Matrix Computations with Randomized Preprocessing
Pan, V. Y., Qian, G., & Zheng, A.-L. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-13182-0_28 · Cited by 4
“(Namely the displacement rank grows by at most q ,c f. [ 10 ].) Then our formal support for the power of our techniques can be automatically extended.”
BackgroundSelf-citationA continuation method for solving symmetric Toeplitz systems
Barel, M. V., Икрамов, Х. Д., & Chesnokov, A. A. (2008) · Computational Mathematics and Mathematical Physics · doi:10.1134/s0965542508120026 · Cited by 4
Simple and Nearly Optimal Polynomial Root-Finding by Means of Root Radii Approximation
Pan, V. Y. (2017) · Springer proceedings in mathematics & statistics · doi:10.1007/978-3-319-56932-1_23 · Cited by 4
Self-citationNearly optimal symbolic-numerical algorithms for structured integer matrices and polynomials
Pan, V. Y., Murphy, B. J., & Rosholt, R. E. (2009) · doi:10.1145/1577190.1577209 · Cited by 4
“Fact 2.3. (See [ p01 , Section 4.2].) We have mM in”
BackgroundMethodInfluentialSelf-citationFast computation of determinants of Bézout matrices and application to curve implicitization
Delvaux, S., Marco, A., ́nez, J.-J. M., et al. (2008) · Linear Algebra and its Applications · doi:10.1016/j.laa.2008.06.027 · Cited by 4
“The relation with other fields of numerical analysis can be studied in [1,15,2,4].”
BackgroundReal and complex polynomial root-finding with eigen-solving and preprocessing
Pan, V. Y., & Zheng, A.-L. (2010) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/1837934.1837978 · Cited by 4
“A matrix r(Fp) has Toeplitz-like structure, has displacement rank at most two, and so can be inverted in O(n log 2 n) ops if it is nonsingular (cf., e.g., [ 20, Chapter 5 ]).”
BackgroundInfluentialSelf-citationDHT-Based Transceivers With Reduced Redundancy
Martins, W. A., & Diniz, P. S. R. (2012) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2012.2212017 · Cited by 4
The generalized reciprocal super Catalan matrix
Kılıç, E., & Arıkan, T. (2016) · TURKISH JOURNAL OF MATHEMATICS · doi:10.3906/mat-1504-100 · Cited by 4
“for more details see [6].”
A Seventh-Order Scheme for Computing the Generalized Drazin Inverse
Ahmed, D., Hama, M. F., Jwamer, K. H. F., et al. (2019) · Mathematics · doi:10.3390/math7070622 · Cited by 4
Fast (Multi-)Evaluation of Linearly Recurrent Sequences: Improvements and ApplicationsPreprint
Ziegler, M. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.cs/0511033 · Cited by 4
“In many of them, the matrix A according to Equation (1) is structured [ 23 ].”
BackgroundMultiplicative Properties of Infinite Block Toeplitz and Hankel Matrices
Gu, C. (2022) · Operator theory · doi:10.1007/978-3-031-13851-5_17 · Cited by 3
Davis, M. M., & Papp, D. (2022) · SIAM Journal on Optimization · doi:10.1137/21m1422574 · Cited by 3
“Therefore the inversion of Λ and the computation of H can be handled using discrete Fourier transforms or the “superfast” (nearly-lineartime) algorithms of Pan and others [28].”
MethodAcceleration of the Inversion of Triangular Toeplitz Matrices and Polynomial Division
Murphy, B. J. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-23568-9_25 · Cited by 3
Inverting Structured Operators Related to Toeplitz Plus Hankel Operators
Kaashoek, M. A., & van Schagen, F. (2013) · Operator theory · doi:10.1007/978-3-0348-0639-8_12 · Cited by 3
On the kernel structure of generalized resultant matrices
Ehrhardt, T., & Rost, K. (2012) · Indagationes Mathematicae · doi:10.1016/j.indag.2012.06.012 · Cited by 3
Exploiting Structures in Weight Matrices for Efficient Real-Time Drone Control with Neural Networks
Kissel, M., Gronauer, S., Korte, M., et al. (2022) · Lecture notes in computer science · doi:10.1007/978-3-031-16474-3_43 · Cited by 3
A Faster Interior-Point Method for Sum-of-Squares Optimization
Jiang, S., Natura, B., & Weinstein, O. (2023) · Algorithmica · doi:10.1007/s00453-023-01112-4 · Cited by 3
“Here, Im ((cid:6)) are all Hankel matrices: We have q = { 1 , x , . . . , x 2 d } and p = { 1 , x , . . . , x d } so for any vector u ∈ R 2 d + 1 we have that These highly structured matrices are known to be invertible in time ˜ O ( d 2 ) (see e.g. [27]).”
BackgroundFaster Numerical Univariate Polynomial Root-Finding by Means of Subdivision Iterations
Luan, Q., Pan, V. Y., Kim, W., & Zaderman, V. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-60026-6_25 · Cited by 4
Self-citationComputational linear algebra over finite fieldsPreprint
Dumas, J., & Pernet, C. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1204.3735 · Cited by 5
“Originating from the seminal paper [33] most of the algorithms dealing with structured matrices use the displacement rank approach [46].”
MethodAn adaptation of the Newton iteration method to solve symmetric positive definite Toeplitz systems
Barel, M. V., & Codevico, G. (2002) · Cited by 3
A Note on Global Newton Iteration Over Archimedean and Non-Archimedean Fields
Hauenstein, J. D., Pan, V. Y., & Szántó, Á. (2014) · Lecture notes in computer science · doi:10.1007/978-3-319-10515-4_15 · Cited by 2
Self-citationBidiagonal Factorizations of Filbert and Lilbert Matrices
Khiar, Y., Mainar, E., Peña, J. M., et al. (2024) · Axioms · doi:10.3390/axioms13040219 · Cited by 2
A Rational Arnoldi Approach for Sobolev Rational Least Squares Problems
Faghih, A., Barel, M. V., Buggenhout, N. V., et al. (2025) · Numerical Linear Algebra with Applications · doi:10.1002/nla.70017 · Cited by 2
Wilber, H., Epperly, E. N., & Barnett, A. H. (2025) · SIAM Journal on Scientific Computing · doi:10.1137/24m1656694 · Cited by 2
Doppler effects on transceivers with reduced redundancy
Gussen, C. M. G., Chaves, R. S., Diniz, P. S. R., et al. (2015) · IEEE International Conference on Digital Signal Processing (DSP) · doi:10.1109/icdsp.2015.7251899 · Cited by 2
The Schur aggregation and solving ill conditioned linear systems: the convergence theorem
Sermé, A., & Richard, J. W. (2012) · Afrika Matematika · doi:10.1007/s13370-012-0066-x · Cited by 2
Superfast Tikhonov Regularization of Toeplitz Systems
Turnes, C. K., Balcan, D. C., & Romberg, J. K. (2014) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2014.2330800 · Cited by 2
Fast Algorithms for Structured Matrix Computations
Stewart, M. (2013) · Discrete mathematics and its applications · doi:10.1201/b16113-73 · Cited by 2
Elimination ideal and bivariate resultant over finite fields
Villard, G. (2023) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/3597066.3597100 · Cited by 2
A Contractive Operator View on an Inversion Formula of Gohberg-Heinig
Frazho, A. E., & Kaashoek, M. A. (2010) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0346-0158-0_11 · Cited by 2
“The literature on this subject is extensive; here we only mention [21], [14], [16, 17], and the books [19], [24] and [25].”
BackgroundQR-factorization of Displacement Structured Matrices Using a Rank Structured Matrix Approach
Delvaux, S., Gemignani, L., & Barel, M. V. (2010) · Birkhäuser Basel eBooks · doi:10.1007/978-3-7643-8996-3_11 · Cited by 2
“[13], the equation (24) transforms then to”
Toeplitz and Toeplitz-block-Toeplitz matrices and their correlation with syzygies of polynomialsPreprint
Khalil, H., Mourrain, B., & Schatzman, M. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0903.1244 · Cited by 2
“The correlation with other types of structured matrices has also been well developed in the literature [10, 9], allowing to treat so efficiently other structures such as Vandermonde or Cauchy-like structures.”
BackgroundRoot-squaring with DPR1 matrices
Pan, V. Y. (2010) · Journal of Mathematical Sciences · doi:10.1007/s10958-010-9993-y · Cited by 2
Self-citationA new method to reduce the complexity of joint detection algorithm
Chen, D., & Saito, T. (2004) · IEEE Global Telecommunications Conference (GLOBECOM) · doi:10.1109/glocom.2003.1258652 · Cited by 2
Chowdhury, M. F. I., Jeannerod, C.-P., Neiger, V., et al. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1402.0643 · Cited by 2
“Our solution to Problem 1 relies on a reduction to a simultaneous approximation problem (Problem 2 below) which generalizes Pad´e and Hermite-Pad´e approximation.”
Random Toeplitz matrices: The condition number under high stochastic dependence
Manrique-Mirón, P. (2021) · Random Matrices Theory and Application · doi:10.1142/s2010326322500277 · Cited by 1
Papliński, J. P., Cariow, A., Strzelec, P., et al. (2024) · Signals · doi:10.3390/signals5030021 · Cited by 1
Randomised subspace system identification: complexities and error bounds
Kedia, V., & Chakraborty, D. (2025) · International Journal of Control · doi:10.1080/00207179.2025.2485169 · Cited by 1
“The computation can be further accelerated by using fast Hankel matrix–vector multiplication (see Table 1.2 p. 4 of Pan, 2001) or by deploying techniques presented in Gall and Urrutia (2018).”
InfluentialPolynomial Evaluation and Interpolation and Transformations of Matrix Structures
Pan, V. Y. (2013) · Lecture notes in computer science · doi:10.1007/978-3-319-02297-0_23 · Cited by 1
Self-citationUsing fast matrix multiplication to solve structured linear systems
Schost, É., Bostan, A., & Jeannerod, C.-P. (2006) · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · doi:10.4230/dagsemproc.06271.16 · Cited by 1
Selecting Algorithms for Black Box Matrices
Eberly, W. (2016) · doi:10.1145/2930889.2930894 · Cited by 1
New Designs for Reduced-Redundancy Transceivers
de Freitas, M. L., Martins, W. A., Filho, E. B. D. L., et al. (2016) · Circuits Systems and Signal Processing · doi:10.1007/s00034-016-0400-x · Cited by 1
Least squares Toeplitz matrix solutions of the matrix equation
Yuan, Y., Zhao, W., & Liu, H. (2016) · Linear and Multilinear Algebra · doi:10.1080/03081087.2016.1261792 · Cited by 1
Root-Finding with Implicit Deflation
Imbach, R., Pan, V. Y., Yap, C. K., et al. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-26831-2_16 · Cited by 1
Self-citationReal Polynomial Root-Finding by Means of Matrix and Polynomial Iterations
Pan, V. Y. (2014) · Lecture notes in computer science · doi:10.1007/978-3-319-10515-4_24 · Cited by 1
Self-citationEfficiency of a 3D Metallic Antenna on top of Finite Ground Plane and Soil
Cavillot, J., Craeye, C., & Acedo, E. D. L. (2022) · International Conference on Electromagnetics in Advanced Applications (ICEAA) · doi:10.1109/iceaa49419.2022.9900015 · Cited by 1
In-place fast polynomial modular remainder
Dumas, J., & Grenet, B. (2024) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/3666000.3669672 · Cited by 1
Integer Levinson Algorithm for the Inversion of Any Nonsingular Hermitian Toeplitz Matrix
Bistritz, Y., & Dekel, I. (2024) · IEEE Transactions on Information Theory · doi:10.1109/tit.2024.3364574 · Cited by 1
Woba, M. D. (2024) · The Review of Contemporary Scientific and Academic Studies · doi:10.55454/rcsas.4.03.2024.003 · Cited by 1
Inversion of centroskewsymmetric Toeplitz-plus-Hankel Bezoutians
Rost, K., & Ehrhardt, T. (2015) · Electronic Journal of Linear Algebra · doi:10.13001/1081-3810.3076 · Cited by 1
“[15],[4], [9], [10], [16], [13], and the references therein).”
Böttcher, A., & Spitkovsky, I. M. (2013) · Discrete mathematics and its applications · doi:10.1201/b16113-26 · Cited by 1
Calculating the Weighted Moore–Penrose Inverse by a High Order Iteration Scheme
Jebreen, H. B. (2019) · Mathematics · doi:10.3390/math7080731 · Cited by 1
Matrix completion for matrices with low-rank displacement
Lazzaro, D., & Morigi, S. (2020) · ETNA - Electronic Transactions on Numerical Analysis · doi:10.1553/etna_vol53s481 · Cited by 1
“In particular, for a square matrix of dimension n and rank r, the asymptotic complexity is O(rn log n); see [33] for details.”
BackgroundMethodA Compact Gradient Based Neural Network for Capon Spectral Estimation
Benchabane, A., & Charif, F. (2020) · International Journal of Neural Networks and Advanced Applications · doi:10.46300/91016.2020.7.7 · Cited by 1
Global Newton Iteration over Archimedean and non-Archimedean FieldsPreprint
Hauenstein, J. D., Pan, V. Y., & Szántó, Á. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1404.5525 · Cited by 1
Self-citationPreconditioning, randomization, solving linear systems, eigen-solving, and root-finding
Pan, V. Y., Qian, G., & Zheng, A.-L. (2009) · doi:10.1145/1577190.1577194 · Cited by 1
Self-citationFFT-Accelerated Iterative MIMO Chip Equalizer Architecture For CDMA Downlink
Guo, Y., McCain, D., & Cavallaro, J. R. (2006) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp.2005.1415882 · Cited by 1
New Structured Matrix Methods for Real and Complex Polynomial Root-findingPreprint
Pan, V. Y., & Zheng, A.-L. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1311.6077 · Cited by 1
Self-citationEfficient Inversion of Rational Maps Over Finite Fields
Cafure, A., Matera, G., & Waissbein, A. (2008) · The IMA volumes in mathematics and its applications · doi:10.1007/978-0-387-75155-9_4 · Cited by 1
Using Toeplitz Matrices to obtain 2D convolutionPreprint
Gnacik, M., & Łapa, K. (2022) · Research Square · doi:10.21203/rs.3.rs-2195496/v1 · Cited by 3
A fast algorithm for decoding algebraic geometry codes with the displacement rank
Fu, X., & You, L. (2011) · International Conference on Information Systems
Extending Cardinal's algorithm to a broader class of structured matrices
Jeannerod, C.-P., Mouilleron, C., & Villard, G. (2010) · ACM communications in computer algebra · doi:10.1145/1823931.1823941
“Although the compression stage can be performed routinely using fast Gaussian elimination (either using randomization [4] or deterministically [6, 2]), suppressing it results in algorithms that are simpler to write and simpler to analyze.”
BackgroundMethodOn the multiplication of scalar and matrix power series with integer coefficients
Buslenko, A. S., & Икрамов, Х. Д. (2008) · Moscow University Computational Mathematics and Cybernetics · doi:10.3103/s0278641908020039
Fast and Numerically Stable Approximate Solution of Trummer’s Problem
Tabanjeh, M. M. (2014) · American Journal of Computational Mathematics · doi:10.4236/ajcm.2014.45033
Sermé, A. (2014) · Afrika Matematika · doi:10.1007/s13370-013-0216-9
Frazho, A. E., Kasshoek, M. A., & Rodman, L. (2010) · IEEE Control Systems · doi:10.1109/mcs.2010.938483
Solving structured linear systems of large displacement rank
Bostan, A., Jeannerod, C.-P., & Schost, É. (2006) · ACM communications in computer algebra · doi:10.1145/1182553.1182558
“These techniques were extended to the other structures presented above; see [ 10 ] for a detailed account.”
MethodSystems of Linear Algebraic Equations
Brezinski, C. (2002) · Numerical methods and algorithms · doi:10.1007/978-1-4613-0261-2_8
Fast recovery and approximation of hidden Cauchy structure
Liesen, J., & Luce, R. (2015) · Linear Algebra and its Applications · doi:10.1016/j.laa.2015.12.002
TR-2008008: Schur Aggregation for Linear Systems and Determinants
Pan, V. Y., Grady, D., Murphy, B. S., et al. (2008) · CUNY Academic Works (City University of New York)
Self-citationRiemannian Optimization for Averaging Positive Definite
Jeuris, B., Vandebril, R., & Nicaise, J. (2015)
An Algorithm for the Vandermonde Matrix-Vector Multiplication with Reduced Multiplicative Complexity
Cariow, A., & Cariowa, G. (2016) · Advances in intelligent systems and computing · doi:10.1007/978-3-319-48429-7_17
Быстрое умножение матриц и смежные вопросы алгебры
Pan, V. Y. (2017) · Математический сборник · doi:10.4213/sm8833 · Cited by 1
Self-citationGradient-Based Neural Network for Superfast Capon Spectral Estimation
Benchabane, A., & Charif, F. (2019) · International Conference on Image and Signal Processing and their Applications (ISPA) · doi:10.1109/ispa48434.2019.8966816
Algebraic Vector SpacesPreprint
Matias, F. M. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2006.03439
On circulant Lyapunov operators, two-variable polynomials, and DFT
Bhawal, C., Pal, D., & Belur, M. N. (2019) · Indian Control Conference · doi:10.1109/icc47138.2019.9123167
Trapdoor Delegation and HIBE from Middle-Product LWE in Standard Model
Le, H. Q., Duong, D. H., Susilo, W., et al. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-57808-4_7
Interpolation by decomposable univariate polynomialsPreprint
Gathen, J. V. Z., & Matera, G. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.15926
Computing the Characteristic Polynomial of Generic Toeplitz-like and Hankel-like Matrices
Karpman, P., Pernet, C., Signargout, H., et al. (2021) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/3452143.3465542
Fast Coefficient Computation for Algebraic Power Series in Positive Characteristic
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Arithmetic Circuits, Structured Matrices and (not so) Deep Learning
Rudra, A. (2022) · Theory of Computing Systems · doi:10.1007/s00224-022-10112-w
The Stability Analysis of Linear Systems with Cauchy—Polynomial-Vandermonde Matrices
Rehman, M.-U., Alzabut, J., Fatima, N., et al. (2023) · Axioms · doi:10.3390/axioms12090831
On Symmetric Factorizations of Hankel Matrices
Ghadiri, M. (2023) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs57990.2023.00127
Kissel, M., & Diepold, K. J. (2024) · Communications in computer and information science · doi:10.1007/978-3-031-74640-6_9
Appendix—Algorithms for (Confluent) Vandermonde Matrices
Respondek, J. S. (2025) · Studies in big data · doi:10.1007/978-3-031-76930-6_11
Dumas, J., & Grenet, B. (2025) · Journal of Symbolic Computation · doi:10.1016/j.jsc.2025.102523
Application of Computer Algebra in List Decoding
Chowdhury, M. F. I. (2013) · Scholarship@Western (Western University)
Efficient computation with structured matrices and arithmetic expressions
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Algorithms for sparse polynomial systems : Gröbner bases and resultants
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Metadata
- Authors
- Pan, V. Y.
- Corresponding author
- Pan, Victor Y.
- ORCID
- Pan, Victor Y.
- Venue
- Birkhäuser Boston eBooks
- Publisher
- Birkhäuser Boston
- Published
- 2001
- OpenAlex
- W21639112
- Cited by
- 203
- References
- 0
- Citations by year
- 2025: 5 · 2024: 8 · 2023: 10 · 2022: 12 · 2021: 9 · 2020: 10 · 2019: 12 · 2018: 2 · 2017: 8 · 2016: 11 · 2015: 10 · 2014: 11 · 2013: 8 · 2012: 12
- FWCI
- 3.51
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Birkhäuser Boston eBooks (publishedVersion)
- International Linear Collider (submittedVersion)
- Funders
- National Science Foundation (9732206)
- City University of New York
- 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
- structured matrices, polynomials, matrix polynomials, structured linear systems
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