References
- A. Björck and V. Pereyra, Solution of Vandermonde systems of equations, Math. Comput. 24 (1970), pp. 893–903. doi: 10.2307/2004623
- T.F. Chan and D.E. Foulser, Effectively well-conditioned linear systems, SIAM J. Sci. Statist. Comput. 9(6) (1988), pp. 963–969. doi: 10.1137/0909067
- N. Cohen and S. De Leo, The quaternionic determinant, Electron. J. Linear Algebra 7 (2000), pp. 100–111. doi: 10.13001/1081-3810.1050
- P.M. Cohn, Skew Field Constructions, Cambridge University Press, Cambridge, 1977.
- A.J. Davies and B.H. McKellar, Non-relativistic quaternionic quantum mechanics, Phys. Rev. A 40 (1989), pp. 4209–4214. doi: 10.1103/PhysRevA.40.4209
- A.J. Davies and B.H. McKellar, Observability of quaternionic quantum mechanics, Phys. Rev. A 46 (1992), pp. 3671–3675. doi: 10.1103/PhysRevA.46.3671
- A.R. De Pierro and M. Wei, Some new properties of the constrained and weighted least squares problem, Linear Algebra Appl. 320 (2000), pp. 145–165. doi: 10.1016/S0024-3795(00)00213-5
- G.M. Dixon, Division Algebras: Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics, Kluwer, Dordrecht, 1994.
- H. Faßender, D.S. Mackey, and N. Hamilton, Jacobi come full circle: Jacobi algorithms for structured Hamiltonian problems, Linear Algebra Appl. 332–334 (2001), pp. 37–80. doi: 10.1016/S0024-3795(00)00093-8
- D. Finkelstein, J.M. Jauch, S. Schiminovich, and D. Speiser, Foundations of quaternion quantum mechanics, J. Math. Phys. 3 (1962), pp. 207–220. doi: 10.1063/1.1703794
- D. Finkelstein, J.M. Jauch, S. Schiminovich, and D. Speiser, Principle of general Q-covariance, J. Math. Phys. 4 (1963), pp. 788–796. doi: 10.1063/1.1724320
- D. Finkelstein, J.M. Jauch, and D. Speiser, Quaternionic representations of compact groups, J. Math. Phys. 4 (1963), pp. 136–140. doi: 10.1063/1.1703880
- D. Finkelstein, J.M. Jauch, and D. Speiser, Notes on Quaternion Quantum Mechanics, Logico-Algebraic Approach to Quantum Mechanics, Vol. II, Reidel, Dordrecht, 1979, pp. 367–421.
- M. Gulliksson, X. Jin, and Y. Wei, Perturbation bounds for constrained and weighted least squares problems, Linear Algebra Appl. 349 (2002), pp. 221–232. doi: 10.1016/S0024-3795(02)00262-8
- F. Gürsey and C.H. Tze, On the Role of Division, Jordan and Related Algebras in Particle Physics, World Scientific, Singapore, 1996.
- Z. Li and H. Huang, Effective condition number for numerical partial differential equations, Numer. Linear Algebra Appl. 15 (2008), pp. 575–594. doi: 10.1002/nla.584
- Z. Li, C.S. Chien, and H.T. Huang, Effective condition number for finite difference method, J. Comput. Appl. Math. 198 (2007), pp. 208–235. doi: 10.1016/j.cam.2005.11.037
- Y. Li, M. Wei, F. Zhang, and J. Zhao, Real structure-preserving algorithms of Householder based transformations for quaternion matrices, J. Comput. Appl. Math. 305(15) (2016), pp. 82–91. doi: 10.1016/j.cam.2016.03.031
- H. Ma, Acute perturbation bounds of weighted Moore-Penrose inverse, Int. J. Comput. Math. 95(4) (2018), pp. 710–720. doi: 10.1080/00207160.2017.1294689
- C.M. Rader and A.O. Steinhardt, Hyperbolic Householder Transformations, IEEE Trans. Acoust. Speech Signal Process. ASSP-34 (1986), pp. 1589–1602. doi: 10.1109/TASSP.1986.1164998
- A.O. Steinhardt, Householder transformations in signal processing, IEEE ASSP Mag. 5(3) (1988), pp. 4–12. doi: 10.1109/53.9259
- G.W. Stewart, On the continuity of the generalized inverse, SIAM J. Appl. Math. 17 (1969), pp. 33–45. doi: 10.1137/0117004
- G.W. Stewart, On the perturbation of pseudo-inverses, projections, and linear least squares problems, SIAM Rev. 19 (1977), pp. 634–662. doi: 10.1137/1019104
- G Wang, Y Wei, and S. Qiao, Generalized Inverses: Theory and Computations, 2nd ed., Developments in Mathematics, Vol. 53, Springer, Singapore, Science Press, Beijing, 2018.
- P.Å. Wedin, Perturbation bounds in connection with the singular value decomposition, BIT 12 (1972), pp. 99–111. doi: 10.1007/BF01932678
- P.Å. Wedin, Perturbation theory for pseudoinverses, BIT 13 (1973), pp. 217–232. doi: 10.1007/BF01933494
- M. Wei, The perturbation of consistent least squares problems, Linear Algebra Appl. 112 (1989), pp. 231–245. doi: 10.1016/0024-3795(89)90598-3
- M. Wei, Equivalent formulae for the supremum and stability of weighted pseudoinverses, Math. Comput. 66(220) (1997), pp. 1487–1508. doi: 10.1090/S0025-5718-97-00899-5
- M. Wei, Supremum and Stability of Weighted Pseudoinverses and Weighted Least Squares Problems: Analysis and Computations, Nova Science Publishers, New York, 2001.
- M. Wei, Relationship between the stiffly weighted pseudoinverse and multi-level constrained pseudoinverse, J. Comput. Math. 22 (2004), pp. 427–436.
- M. Wei, On stable perturbations of the stiffly weighted pseudoinverse and weighted least squares problem, J. Comput. Math. 23(5) (2005), pp. 527–536.
- M. Wei, Theory and Computations of Generalized Least Squares Problems (in Chinese), Science Press, Beijing, 2006.
- Y. Wei, T. Lu, T. Hung, and Z. Li, Effective condition number for weighted linear least squares problems and applications to the Trefftz method, Eng. Anal. Bound. Elem. 36 (2012), pp. 53–62. doi: 10.1016/j.enganabound.2011.07.010
- M. Wei, Y. Li, F. Zhang, and J. Zhao, Quaternion Matrix Computations, Nova Science Publisher, New York, 2018.
- P. Xie, H. Xiang, and Y. Wei, A contribution to perturbation analysis for total least squares problems, Numer. Algorithms 75 (2017), pp. 381–395. doi: 10.1007/s11075-017-0285-1
- P. Xie, H. Xiang, and Y. Wei, Randomized algorithms for total least squares problems, Numer. Linear Algebra Appl. 26 (2019), p. e2219. doi: 10.1002/nla.2219
- F. Zhang, Quaternions and matrices of quaternions, Linear Algebra Appl. 251 (1997), pp. 21–57. doi: 10.1016/0024-3795(95)00543-9