W. A. Adkins and S. H. Weintraub, Algebra: An approach via module theory, Graduate Texts in Mathematics, 136, Springer, New York, 1992.
D. Bini and M. Capovani, “Tensor rank and border rank of band Toeplitz matrices,” SIAM J. Comput., 16 (1987), no. 2, pp. 252–258.
Å. Björck, Numerical Methods for Least Squares Problems, SIAM, Philadelphia, PA, 1996.
J.-L. Brylinski, “Algebraic measures of entanglement,” pp. 3–23, G. Chen and R. K. Brylinski (Eds), Mathematics of Quantum Computation, CRC, Boca Raton, FL, 2002.
J. Buczyński and J. M. Landsberg, “Ranks of tensors and a generalization of secant varieties,” Linear Algebra Appl., 438 (2013), no. 2, pp. 668–689.
P. Bürgisser, M. Clausen, and M. A. Shokrollahi, Algebraic Complexity Theory, Grundlehren der Mathematischen Wissenschaften, 315, Springer-Verlag, Berlin, 1997.
R. H.-F. Chan and X.-Q. Jin, An Introduction to Iterative Toeplitz Solvers, Fundamentals of Algorithms, 5, SIAM, Philadelphia, PA, 2007.
H. Cohn, R. Kleinberg, B. Szegedy, and C. Umans, “Group-theoretic algorithms for matrix multiplication,” Proc. IEEE Symp. Found. Comput. Sci. (FOCS), 46 (2005), pp. 379–388.
H. Cohn and C. Umans, “A group-theoretic approach to fast matrix multiplication,” Proc. IEEE Symp. Found. Comput. Sci. (FOCS), 44 (2003), pp. 438–449.
H. Cohn and C. Umans, “Fast matrix multiplication using coherent configurations,” Proc. ACM–SIAM Symp. Discrete Algorithms (SODA), 24 ( 2013), pp. 1074–1087.
S. A. Cook, On the Minimum Computation Time of Functions, Ph.D. thesis, Harvard University, Cambridge, MA, 1966.
J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comp., 19 (1965), no. 90, pp. 297–301.
D. Coppersmith and S. Winograd, “Matrix multiplication via arithmetic progressions,” J. Symbolic Comput., 9 (1990), no. 3, pp. 251–280.
P. J. Davis, Circulant Matrices, John Wiley, New York, NY, 1979.
V. De Silva and L.-H. Lim, “Tensor rank and the ill-posedness of the best low-rank approximation problem,” SIAM J. Matrix Anal. Appl., 30 (2008), no. 3, pp. 1084–1127.
J. Demmel, I. Dumitriu, O. Holtz, and R. Kleinberg, “Fast matrix multiplication is stable,” Numer. Math., 106 (2007), no. 2, pp. 199–224.
S. Friedland and L.-H. Lim, “Nuclear norm of higher-order tensors,” (2016). http://arxiv.org/abs/1410.6072.
M. Fürer, “Faster integer multiplication,” SIAM J. Comput., 39 (2009), no. 3, pp. 979–1005.
G. Golub and C. Van Loan, Matrix Computations, 4th Ed., Johns Hopkins University Press, Baltimore, MD, 2013.
N. J. Higham, Accuracy and Stability of Numerical Algorithms, 2nd Ed., SIAM, Philadelphia, PA, 2002.
N. J. Higham, Functions of Matrices, SIAM, Philadelphia, PA, 2008.
N. J. Higham, “Stability of a method for multiplying complex matrices with three real matrix multiplications,” SIAM J. Matrix Anal. Appl., 13 (1992), no. 3, pp. 681–687.
Intel 64 and IA-32 Architectures Optimization Reference Manual, September 2015. http://www.intel.com/content/dam/www/public/us/en/documents/manuals/64-ia-32-architectures-optimization-manual
T. Kailath and J. Chun, “Generalized displacement structure for block-Toeplitz, Toeplitz-block, and Toeplitz-derived matrices,” SIAM J. Matrix Anal. Appl., 15 (1994), no. 1, pp. 114–128.
A. Karatsuba and Yu. Ofman, “Multiplication of many-digital numbers by automatic computers,” Dokl. Akad. Nauk SSSR, 145 (1962), pp. 293–294 [English translation: Soviet Phys. Dokl., 7 (1963), pp. 595–596].
D. E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical algorithms, 3rd Ed., Addison–Wesley, Reading, MA, 1998.
V. K. Kodavalla, “IP gate count estimation methodology during micro-architecture phase,” IP Based Electronic System Conference and Exhibition (IP-SOC), Grenoble, France, December 2007. http://www.design-reuse.com/articles/19171/ip-gate-count-estimation-micro-architecture-phase.html
J. M. Landsberg, Tensors: Geometry and Applications, Graduate Studies in Mathematics, 128, AMS, Providence, RI, 2012.
S. Lang, Algebra, Rev. 3rd Ed., Graduate Texts in Mathematics, 211, Springer, New York, NY, 2002.
F. Le Gall, “Powers of tensors and fast matrix multiplication,” Proc. Internat. Symp. Symbolic Algebr. Comput. (ISSAC), 39 (2014), pp. 296–303.
L.-H. Lim, “Tensors and hypermatrices,” in: L. Hogben (Ed.), Handbook of Linear Algebra, 2nd Ed., CRC Press, Boca Raton, FL, 2013.
J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, Rev. Ed., Graduate Studies in Mathematics, 30, AMS, Providence, RI, 2001.
W. Miller, “Computational complexity and numerical stability,” SIAM J. Comput., 4 (1975), no. 2, pp. 97–107.
M. K. Ng, Iterative Methods for Toeplitz Systems, Oxford University Press, New York, NY, 2004.
G. Ottaviani, “Symplectic bundles on the plane, secant varieties and Lüroth quartics revisited,” Quad. Mat., 21 (2007), pp. 315–352.
V. Y. Pan, Structured Matrices and Polynomials: Unified superfast algorithms, Birkhäuser, Boston, MA, 2001.
A. Schönhage, “Partial and total matrix multiplication,” SIAM J. Comput., 10 (1981), no. 3, pp. 434–455.
A. Schönhage and V. Strassen, “Schnelle Multiplikation großer Zahlen,” Computing, 7 (1971), no. 3, pp. 281–292.
G. Strang and S. MacNamara, “Functions of difference matrices are Toeplitz plus Hankel,” SIAM Rev., 56 (2014), no. 3, pp. 525–546.
V. Strassen, “Gaussian elimination is not optimal,” Numer. Math., 13 (1969), no. 4, pp. 354–356.
V. Strassen, “Rank and optimal computation of generic tensors,” Linear Algebra Appl., 52/53 (1983), pp. 645–685.
V. Strassen, “Relative bilinear complexity and matrix multiplication,” J. Reine Angew. Math., 375/376 (1987), pp. 406–443.
V. Strassen, “Vermeidung von Divisionen,” J. Reine Angew. Math., 264 (1973), pp. 184–202.
A. L. Toom, “The complexity of a scheme of functional elements realizing the multiplication of integers,” Dokl. Akad. Nauk SSSR, 150 (1963), pp. 496–498 [English translation: Soviet Math. Dokl., 4 (1963), pp. 714–716].
C. F. Van Loan, “The ubiquitous Kronecker product,” J. Comput. Appl. Math., 123 (2000), no. 1–2, pp. 85–100.
V. Vassilevska Williams, “Multiplying matrices faster than Coppersmith–Winograd,” Proc. ACM Symp. Theory Comput. (STOC), 44 (2012), pp. 887–898.
D. S. Watkins, The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods, SIAM, Philadelphia, PA, 2007.
S. Winograd, “Some bilinear forms whose multiplicative complexity depends on the field of constants,” Math. Syst. Theory, 10 (1976/77), no. 2, pp. 169–180.
K. Ye and L.-H. Lim, “Algorithms for structured matrix-vector product of optimal bilinear complexity,” Proc. IEEE Inform. Theory Workshop (ITW), 16 (2016), to appear.
K. Ye and L.-H. Lim, “Every matrix is a product of Toeplitz matrices,” Found. Comput. Math., 16 (2016), no. 3, pp. 577–598.