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Structured Matrices and Polynomials
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Efficient Public Key Encryption Based on Ideal Lattices
Stehlé, D., Steinfeld, R., Tanaka, K., & Xagawa, K. (2009) · Lecture notes in computer science · doi:10.1007/978-3-642-10366-7_36 · Cited by 371
Henzinger, M. R., Forster, S., Nanongkai, D., & Saranurak, T. (2015) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/2746539.2746609 · Cited by 273
Algebraic Signal Processing Theory: Foundation and 1-D Time
Püschel, M., & Moura, J. M. F. (2008) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2008.925261 · Cited by 174
Structured Transforms for Small-Footprint Deep LearningPreprint
Sindhwani, V., Sainath, T. N., & Kumar, S. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1510.01722 · Cited by 200
“Fast numerical linear algebra algorithms extend to such matrices [18].”
BackgroundInfluentialApproximate iterations for structured matrices
Hackbusch, W., Khoromskij, B. N., & Tyrtyshnikov, E. E. (2008) · Numerische Mathematik · doi:10.1007/s00211-008-0143-0 · Cited by 86
Computation of Approximate Polynomial GCDs and an Extension
Pan, V. Y. (2001) · Information and Computation · doi:10.1006/inco.2001.3032 · Cited by 80
Self-citationPan, V. Y. (2001) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/384101.384136 · Cited by 66
“E) in [4, chapter 1]) or Problem 2.9.2 in [ 32 ] for the input polynomialMu j(x) mod xn+1 to obtain the polynomials F u j = F u j(x) (approximating Fu j), G u j( x), and thus G u j = G u j(x) (approximating Gu j) such that”
BackgroundInfluentialSelf-citationLearning compact recurrent neural networks
Lu, Z., Sindhwani, V., & Sainath, T. N. (2016) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp.2016.7472821 · Cited by 89
“Recently, [10] proposed a new family of parameter sharing schemes for small-footprint deep learning based on structured matrices characterized by the notion of displacement operators [16].”
BackgroundLü, X., Pang, H., & Sun, H. (2015) · Numerical Linear Algebra with Applications · doi:10.1002/nla.1972 · Cited by 63
Superfast Approximative Implementation of the IAA Spectral Estimate
Glentis, G.-O., & Jakobsson, A. (2011) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2011.2170979 · Cited by 63
Solving structured linear systems with large displacement rank
Bostan, A., Jeannerod, C.-P., & Schost, É. (2008) · Theoretical Computer Science · doi:10.1016/j.tcs.2008.05.014 · Cited by 49
“7 in [45] shows that the unique matrix A ∈ K such that ∆[D(x),D(y)](A) = GH is A = ∑α i=1 D(gi) C(x, y) D(hi).”
BackgroundInfluentialNew progress in real and complex polynomial root-finding
Pan, V. Y., & Zheng, A.-L. (2011) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2010.12.070 · Cited by 50
Self-citationSum-of-Squares Optimization without Semidefinite Programming
Papp, D., & Yıldız, S. (2019) · SIAM Journal on Optimization · doi:10.1137/17m1160124 · Cited by 48
“The inverse of a positive definite Hankel matrix can be computed in O ( d 2 ) time using specialized algorithms such as those described in [25] and [48, Ch. 5].”
MethodStructured matrices and Newton's iteration: unified approach
Pan, V. Y., Rami, Y., & Wang, X. (2002) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(01)00336-6 · Cited by 44
“We refer the reader to [4, 32 ] on property (3), will specify properties (1) and (2) in”
BackgroundMethodResultInfluentialSelf-citationOptimal Designs for Rational Function Regression
Papp, D. (2012) · Journal of the American Statistical Association · doi:10.1080/01621459.2012.656035 · Cited by 43
Schur aggregation for linear systems and determinants
Pan, V. Y., Grady, D., Murphy, B. S., et al. (2008) · Theoretical Computer Science · doi:10.1016/j.tcs.2008.09.005 · Cited by 40
Self-citationFast algorithms for Toeplitz and Hankel matrices
Heinig, G., & Rost, K. (2011) · Linear Algebra and its Applications · doi:10.1016/j.laa.2010.12.001 · Cited by 40
“We refer the reader who is interested in numerical aspects to the books [17,5,39,32,4] and the references therein.”
BackgroundBlock-encoding-based quantum algorithm for linear systems with displacement structures
Wan, L., Yu, C., Pan, S., Qin, S., Gao, F., & Wen, Q. (2021) · Physical Review A · doi:10.1103/physreva.104.062414 · Cited by 39
Inversion of Displacement Operators
Pan, V. Y., & Wang, X. (2003) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s089547980238627x · Cited by 39
Self-citationSMASH: Structured matrix approximation by separation and hierarchy
Cai, D., Chow, E., Erlandson, L., Saad, Y., & Xi, Y. (2018) · Numerical Linear Algebra with Applications · doi:10.1002/nla.2204 · Cited by 36
A Higher Order Iterative Method for Computing the Drazin Inverse
Soleymani, F., & Stanimirović, P. S. (2013) · The Scientific World JOURNAL · doi:10.1155/2013/708647 · Cited by 36
Algebraic Signal Processing Theory: 1-D Nearest Neighbor Models
Sandryhaila, A., Kovačević, J., & Püschel, M. (2012) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2012.2186133 · Cited by 36
X-Secure T-Private Federated Submodel Learning With Elastic Dropout Resilience
Jia, Z., & Jafar, S. A. (2022) · IEEE Transactions on Information Theory · doi:10.1109/tit.2022.3165400 · Cited by 35
Chowdhury, M. F. I., Jeannerod, C.-P., Neiger, V., Schost, É., & Villard, G. (2015) · IEEE Transactions on Information Theory · doi:10.1109/tit.2015.2416068 · Cited by 32
“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.”
Computations with quasiseparable polynomials and matrices
Bella, T., Eidelman, Y., Gohberg, I., et al. (2008) · Theoretical Computer Science · doi:10.1016/j.tcs.2008.09.008 · Cited by 34
“An interplay between polynomials and structured matrices is a well-studied topic, see, e.g., [ 47 , 43, 44, 45] and many references therein.”
BackgroundAcceleration of Euclidean algorithm and extensions
Pan, V. Y., & Wang, X. (2002) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/780506.780533 · Cited by 31
Self-citationList-Decodable Coded Computing: Breaking the Adversarial Toleration Barrier
Soleymani, M., Ali, R. E., Mahdavifar, H., & Avestimehr, A. S. (2021) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit45174.2021.9518044 · Cited by 27
Recycling Randomness with Structure for Sublinear time Kernel ExpansionsPreprint
Choromański, K., & Sindhwani, V. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1605.09049 · Cited by 30
“We note in passing that the displacement rank framework generalizes to other types of base structures (e.g. Vandermonde); see (Pan, 2001).”
BackgroundMethodInfluentialHomotopic residual correction processes
Pan, V. Y., Kunin, M., Rosholt, R. E., et al. (2005) · Mathematics of Computation · doi:10.1090/s0025-5718-05-01771-0 · Cited by 29
“For the operators L associated with the Toeplitz/Hankel structure, we have � L−1� = O(n) (see the estimates for these and other inverse displacement operators L−1 in [ P01a , Section 6.4], [PW03]).”
InfluentialSelf-citationThe amended DSeSC power method for polynomial root-finding
Pan, V. Y. (2005) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2004.09.011 · Cited by 27
Self-citationFast Solvers for Dense Linear Systems
Kauers, M. (2008) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/j.nuclphysbps.2008.09.111 · Cited by 26
“If, in the example, we had chosen 2 ·(114, 108, 125, 1) = (97, 85, 119, 2) as the first solution (after all, the solution of a linear system is not unique), then the algorithm would never have terminated.”
MethodBlock-Based Transceivers With Minimum Redundancy
Martins, W. A., & Diniz, P. S. R. (2009) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2009.2033000 · Cited by 26
Iterative inversion of structured matrices
Pan, V. Y., Barel, M. V., Wang, X., et al. (2004) · Theoretical Computer Science · doi:10.1016/j.tcs.2004.01.008 · Cited by 26
“cified in [17,19,16,18] and [8, Chapter 6]. (See also the homotopy/continuation approach in [ 8, Chapter 6 ] and [16].) There are certain policies allowing convergence acceleration, such as”
BackgroundMethodInfluentialSelf-citationDarsena, D., Gelli, G., Melito, F., et al. (2015) · IEEE Signal Processing Letters · doi:10.1109/lsp.2015.2398366 · Cited by 25
Huang, R. (2019) · Mathematics of Computation · doi:10.1090/mcom/3444 · Cited by 26
Root-Finding with Eigen-Solving
Pan, V. Y., Murphy, B. J., Rosholt, R. E., et al. (2007) · Birkhäuser Basel eBooks · doi:10.1007/978-3-7643-7984-1_12 · Cited by 25
Self-citationFast Structured Matrix Computations: Tensor Rank and Cohn–Umans Method
Ye, K., & Lim, L. (2016) · Foundations of Computational Mathematics · doi:10.1007/s10208-016-9332-x · Cited by 21
An improved Schulz-type iterative method for matrix inversion with application
Haghani, F. K., & Soleymani, F. (2014) · Transactions of the Institute of Measurement and Control · doi:10.1177/0142331214528350 · Cited by 22
“Hopefully, this need was fulfilled by some pioneer works in the literature (Pan, 2001) through providing some appropriate initial approximations.”
BackgroundInfinite triangular matrices, q-Pascal matrices, and determinantal representations
Verde‐Star, L. (2010) · Linear Algebra and its Applications · doi:10.1016/j.laa.2010.08.022 · Cited by 21
“See [6].”
Newton-Like Iteration Based on a Cubic Polynomial for Structured Matrices
Codevico, G., Pan, V. Y., & Barel, M. V. (2004) · Numerical Algorithms · doi:10.1007/s11075-004-3996-z · Cited by 20
Self-citationDisplacement rank of the Drazin inverse
Diao, H., Wei, Y., & Qiao, S. (2004) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2003.09.050 · Cited by 20
Direct versus iterative methods for fixed-point implementation of matrix inversion
Ylinen, M., Burian, A., & Takala, J. (2004) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2004.1328724 · Cited by 20
Additive Preconditioning for Matrix Computations
Pan, V. Y., Ivolgin, D., Murphy, B. J., et al. (2008) · Springer eBooks · doi:10.1007/978-3-540-79709-8_37 · Cited by 20
Self-citationHuang, R. (2017) · Journal of Scientific Computing · doi:10.1007/s10915-017-0584-7 · Cited by 19
Olshevsky, V., Oseledets, I. V., & Tyrtyshnikov, E. E. (2007) · Birkhäuser Basel eBooks · doi:10.1007/978-3-7643-8539-2_14 · Cited by 18
Displacement structure of group inverses
Wei, Y., & Ng, M. K. (2004) · Numerical Linear Algebra with Applications · doi:10.1002/nla.405 · Cited by 17
Fast conversion algorithms for orthogonal polynomials
Bostan, A., Salvy, B., & Schost, É. (2009) · Linear Algebra and its Applications · doi:10.1016/j.laa.2009.08.002 · Cited by 16
Block Transceivers: OFDM and Beyond
Diniz, P. S. R., Martins, W. A., & Lima, M. V. S. (2012) · Synthesis lectures on communications · doi:10.2200/s00424ed1v01y201206com007 · Cited by 16
Accelerated Solution of Multivariate Polynomial Systems of Equations
Mourrain, B., Pan, V. Y., & Ruatta, O. (2003) · SIAM Journal on Computing · doi:10.1137/s0097539701385168 · Cited by 16
Self-citationStudying new generalizations of Max-Min matrices with a novel approach
Kılıç, E., & Arıkan, T. (2019) · TURKISH JOURNAL OF MATHEMATICS · doi:10.3906/mat-1811-95 · Cited by 15
Multi-dimensional Capon spectral estimation using discrete Zhang neural networks
Benchabane, A., Bennia, A., Charif, F., et al. (2012) · Multidimensional Systems and Signal Processing · doi:10.1007/s11045-012-0189-0 · Cited by 15
“The signal x ( n ) is modeled as (Capon 1969; Li et al. 1998; Pan 2001): where α(ω) denotes the complex amplitude of the sinusoidal component at frequency ω , and e ( n ) denotes the residual term which includes the un-modeled noise and interference from frequencies other than ω .”
BackgroundWiener–Hopf and spectral factorization of real polynomials by Newton’s method
Böttcher, A., & Halwaß, M. (2013) · Linear Algebra and its Applications · doi:10.1016/j.laa.2013.02.020 · Cited by 15
Pan, V. Y. (2006) · Journal of Mathematical Sciences · doi:10.1007/s10958-006-0118-6 · Cited by 14
Self-citationAn Algorithm for Transforming Regular Chain into Normal Chain
Li, B., & Wang, D. (2008) · Lecture notes in computer science · doi:10.1007/978-3-540-87827-8_20 · Cited by 13
“Another proof of this theorem also can be found in [ 7 ].”
ResultA Parallel Structured Divide-and-Conquer Algorithm for Symmetric Tridiagonal Eigenvalue Problems
Liao, X., Li, S., Lu, Y., et al. (2020) · IEEE Transactions on Parallel and Distributed Systems · doi:10.1109/tpds.2020.3019471 · Cited by 13
Rost, K. (2010) · Birkhäuser Basel eBooks · doi:10.1007/978-3-7643-8996-3_3 · Cited by 13
“(This list is far away from being complete!) Books: Gohberg, Lancaster, and Rodman [10], Heinig and Rost [33], Lancaster and Tismenetsky [54], Bini and Pan [2], Fuhrmann [6], Pan [62], Lascoux [56].”
BackgroundSuboptimal Linear MMSE Equalizers With Minimum Redundancy
Martins, W. A., & Diniz, P. S. R. (2010) · IEEE Signal Processing Letters · doi:10.1109/lsp.2010.2042515 · Cited by 13
A superfast solver for real symmetric Toeplitz systems using real trigonometric transformations
Codevico, G., Heinig, G., & Barel, M. V. (2005) · Numerical Linear Algebra with Applications · doi:10.1002/nla.445 · Cited by 13
“SUPERFAST SOLVER FOR REAL SYMMETRIC TOEPLITZ SYSTEMS 1 papers (see [ 13 ]).”
BackgroundNew Fast Algorithms for Toeplitz-Plus-Hankel Matrices
Heinig, G., & Rost, K. (2003) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479802410074 · Cited by 13
LTI Transceivers With Reduced Redundancy
Martins, W. A., & Diniz, P. S. R. (2011) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2011.2174056 · Cited by 12
Solving toeplitz- and vandermonde-like linear systems with large displacement rank
Bostan, A., Jeannerod, C.-P., & Schost, É. (2007) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/1277548.1277554 · Cited by 12
“Since then, the literature has vastly developed; see [36] for a list of references.”
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Cavillot, J., Bodehou, M., Hubert, S., et al. (2021) · IEEE Transactions on Antennas and Propagation · doi:10.1109/tap.2021.3111305 · Cited by 12
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
On the complexities of multipoint evaluation and interpolation
Bostan, A., & Schost, É. (2004) · Theoretical Computer Science · doi:10.1016/j.tcs.2004.09.002 · Cited by 11
“(1) To solve this question, we use a reduction that appeared in (Kaltofen and Yagati, 1989) (see also (Pan, 2001) for an alternative formula originating from (Gohberg and Olshevsky, 1994a), which requires essentially the same operations).”
MethodChallapalle, N. R., Rampalli, S., Chandran, M., Kalsi, G. S., Subramoney, S., Sampson, J., & Narayanan, V. (2020) · Design, Automation, and Test in Europe · doi:10.23919/date48585.2020.9116469 · Cited by 10
“The block circulant property is used to speed-up matrix operations such as multiplication and eigen value decomposition [18].”
MethodStatistical properties of structured random matrices
Bogomolny, E., & Giraud, O. (2021) · Physical review. E · doi:10.1103/physreve.103.042213 · Cited by 12
Fast Approximate Computations with Cauchy Matrices, Polynomials and Rational Functions
Pan, V. Y. (2014) · Lecture notes in computer science · doi:10.1007/978-3-319-06686-8_22 · Cited by 11
Self-citationRandomized Matrix ComputationsPreprint
Pan, V. Y., Qian, G., & Zheng, A.-L. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1210.7476 · Cited by 11
Self-citationQuasi-optimal Multiplication of Linear Differential Operators
Benoit, A., Bostan, A., & van der Hoeven, J. (2012) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2012.57 · Cited by 10
“in Kr×r), and for most of them, in a quasi-linear way [2, 4, 8, 24, 14].”
BackgroundStructured Matrices and Their Application in Neural Networks: A Survey
Kissel, M., & Diepold, K. J. (2023) · New Generation Computing · doi:10.1007/s00354-023-00226-1 · Cited by 9
Old and New Nearly Optimal Polynomial Root-Finders
Pan, V. Y. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-26831-2_26 · Cited by 11
Self-citationPractical Divide-and-Conquer Algorithms for Polynomial Arithmetic
Hart, W. B., & Novocin, A. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-23568-9_16 · Cited by 10
The reciprocal super Catalan matrix
Prodinger, H. (2015) · Special Matrices · doi:10.1515/spma-2015-0010 · Cited by 8
Displacement structure of the core inverse
Ma, H. (2020) · Linear and Multilinear Algebra · doi:10.1080/03081087.2020.1716677 · Cited by 8
Exploiting higher computational efficiency index for computing outer generalized inverses
Ma, X., Nashine, H. K., Shil, S., et al. (2022) · Applied Numerical Mathematics · doi:10.1016/j.apnum.2022.01.017 · Cited by 8
Resultant matrices and inversion of Bezoutians
Ehrhardt, T., & Rost, K. (2012) · Linear Algebra and its Applications · doi:10.1016/j.laa.2012.08.021 · Cited by 8
Simulation of Gaussian Random Fields With One Derivative
Stein, M. L. (2011) · Journal of Computational and Graphical Statistics · doi:10.1198/jcgs.2010.10069 · Cited by 8
“…N × N Toeplitz matrices, there are O(N log β N) noniterative algorithms for carrying out these recursions (with, e.g., β = 2; see Ammar and Gragg 1988 or Pan 2001), so there may be block versions of these approaches yielding O(N 4 log β N) algorithms, but I have been unable to locate a published…”
MethodAn efficient quadratically convergent iterative method to find the Moore–Penrose inverse
Esmaeili, H., & Pirnia, A. (2016) · International Journal of Computer Mathematics · doi:10.1080/00207160.2016.1167883 · Cited by 8
“A discussion on choosing the initial approximation X0 is given in [2,11].”
BackgroundSplit algorithms for skewsymmetric Toeplitz matrices with arbitrary rank profile
Heinig, G., & Rost, K. (2004) · Theoretical Computer Science · doi:10.1016/j.tcs.2004.01.003 · Cited by 8
“Note also that formula (2) can be written in terms of polynomial multiplication, and polynomial multiplication can be carried out with complexity O( N log N log log N ) in any ’eld (see [17] and references therein).”
BackgroundSpectral-DP: Differentially Private Deep Learning through Spectral Perturbation and Filtering
Feng, C., Xu, N., Wen, W., Venkitasubramaniam, P., & Ding, C. (2023) · IEEE Symposium on Security and Privacy (S&P) · doi:10.1109/sp46215.2023.10179457 · Cited by 9
Computing specified generators of structured matrix inverses
Jeannerod, C.-P., & Mouilleron, C. (2010) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/1837934.1837988 · Cited by 7
“All of them appear in/follow immediately from [18, 19].”
BackgroundInfluentialModeling circulating cavity fields using the discrete linear canonical transform
Ciobanu, A. A., Brown, D. D., Veitch, P. J., et al. (2021) · Journal of the Optical Society of America A · doi:10.1364/josaa.433575 · Cited by 7
A note on computing the inverse of a triangular Toeplitz matrix
Belhaj, S., & Dridi, M. (2014) · Applied Mathematics and Computation · doi:10.1016/j.amc.2014.03.077 · Cited by 7
“Problems related to compute the inverse of a nonsingular lower triangular Toeplitz matrix often appear in several fundame ntal problems of scientific computing, signal and image processing, etc [8].”
BackgroundA fast method to block-diagonalize a Hankel matrix
Belhaj, S. (2007) · Numerical Algorithms · doi:10.1007/s11075-007-9144-9 · Cited by 7
Algorithms for Structured Linear Systems Solving and Their Implementation
Hyun, S. G., Lebreton, R., & Schost, É. (2017) · International Symposium on Symbolic and Algebraic Computation · doi:10.1145/3087604.3087659 · Cited by 7
“2 in [39] shows that if a, u consist of 2m distinct scalars, and b, v consist of 2n distinct scalars, then there exists a non-zero polynomial ∆ in the entries of x and y, of degree at most μ = min(m,n) in each block of variables, such that the non-vanishing of ∆ implies that A′ has generic rank prole (that theorem is…”
BackgroundMethodInfluentialFast matrix multiplication and its algebraic neighbourhood
Pan, V. Y. (2017) · Sbornik Mathematics · doi:10.1070/sm8833 · Cited by 9
Self-citationTrapdoor Delegation and HIBE from Middle-Product LWE in Standard Model
Le, H. Q., Duong, D. H., Susilo, W., et al. (2020) · Research Online (University of Wollongong) · Cited by 7
Efficient Identification of Butterfly Sparse Matrix Factorizations
Zheng, L., Riccietti, E., & Gribonval, R. (2023) · SIAM Journal on Mathematics of Data Science · doi:10.1137/22m1488727 · Cited by 7
Fast simulation technique for antenna installed on a finite ground plane
Cavillot, J., Tihon, D., Craeye, C., et al. (2019) · International Conference on Electromagnetics in Advanced Applications (ICEAA) · doi:10.1109/iceaa.2019.8879358 · Cited by 7
Soleymani, F., Sharifi, M., & Shateyi, S. (2014) · Journal of Applied Mathematics · doi:10.1155/2014/731562 · Cited by 6
The asymptotic distribution of the condition number for random circulant matrices
Barrera, G., & Manrique-Mirón, P. (2022) · Extremes · doi:10.1007/s10687-022-00442-w · Cited by 6
Real block-circulant matrices and DCT-DST algorithm for transformer neural network
Asriani, E., Muchtadi-Alamsyah, I., & Purwarianti, A. (2023) · Frontiers in Applied Mathematics and Statistics · doi:10.3389/fams.2023.1260187 · Cited by 5
A Simplified Architecture of the Zhang Neural Network for Toeplitz Linear Systems Solving
Charif, F., Benchabane, A., & Bennia, A. (2017) · Neural Processing Letters · doi:10.1007/s11063-017-9656-9 · Cited by 6
Unified Nearly Optimal Algorithms for Structured Integer Matrices
Pan, V. Y., Murphy, B. J., & Rosholt, R. E. (2010) · Birkhäuser Basel eBooks · doi:10.1007/978-3-7643-8996-3_16 · Cited by 6
“In view of our results in the previous section, this includes the transposes, blocks and inverses of the latter matrices, as well as the products, sums, and linear combinations of pairs of such matrices for the same or properly reconciled operators (see Theorems 2.2–2.4 and [ P01 , Chapter 4]).”
BackgroundMethodInfluentialSelf-citationOn the hardness of approximating the permanent of structured matrices
Codenotti, B., Shparlinski, J. D., & Winterhof, A. (2002) · Computational Complexity · doi:10.1007/s00037-002-0174-3 · Cited by 6
“V. Pan (2001).”
BackgroundPilot-aided designs of memoryless block equalizers with minimum redundancy
Martins, W. A., & Diniz, P. S. R. (2010) · doi:10.1109/iscas.2010.5537975 · Cited by 6
Topics in the numerical linear algebra of Toeplitz and Hankel matrices
Böttcher, A., & Rost, K. (2004) · GAMM-Mitteilungen · doi:10.1002/gamm.201490009 · Cited by 6
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
Efficient reformulation of image reconstruction with compressive sensing
Muqaibel, A. H. (2017) · AEU - International Journal of Electronics and Communications · doi:10.1016/j.aeue.2017.03.017 · Cited by 5
Generalized Matrix Nearness Problems
Li, Z., & Lim, L. (2023) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/22m1526034 · Cited by 5
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
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 ›
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