Publications and Preprints

Submitted/Preprints  (Brief summary)
  1. Superfast and stable structured solvers for Toeplitz least squares via randomized sampling, with Y. Xi, S. Cauley, and V. Balakrishnan,  under revision, SIAM J. Matrix Anal. Appl., 2012.
  2. Efficient scalable algorithms for solving linear systems with hierarchically semiseparable structures, with M. V. de Hoop, X. S. Li, Y. Situ, and S. Wang, revised, SIAM J. Sci. Comput., 2012 (an earlier report)
  3. A fast structured eigensolver for symmetric Toeplitz matrices and more via adaptive randomized sampling, submitted, SIAM J. Matrix Anal. Appl., 2013.
  4. Error bounds for explicit ERKN methods for systems of oscillatory second-order differential equations, with B. Wang and X. Wu, submitted, 2012.
  5. Symplecticity and symmetry for multidimensional ERKN integrators for multi-frequency and multidimensional oscillatory systems, with B. Wang and X. Wu, submitted, 2012.
  6. Fast structured solvers for finding the eigenvalues of large structured matrices, with Y. Xi, preprint.
  7. Efficient matrix-free preconditioning techniques for augmented immersed interface method, with Z. Li, preprint.
  8. An arbitrary inversion algorithm for large sparse matrices, with Y. Xi, preprint.
  9. Scalable direct solvers for large banded linear systems and their applications, with V. Balakrishnan, and S. Cauley, D. Imberti, preprint.
  10. A highly efficient stable and superfast Toeplitz solver, with M. Gu, preprint.
  11. Robust symmetric SPIKE algorithm for large banded SPD matrices, preprint.
Papers  (Brief summary; Google Scholar citations)
  1. J. Xia, Randomized sparse direct solvers,
    SIAM J. Matrix Anal. Appl., 34 (2013), pp. 197-227. (PDF. Journal article link)
  2. J. Xia, Efficient structured multifrontal factorization for general large sparse matrices,
    SIAM J. Sci. Comput., 35 (2013), pp. A832-A860. (PDF. Journal article link)
    3.
  3. S. Wang, M. V. de Hoop, J. Xia, and X. S. Li, Massively parallel structured multifrontal solver for time-harmonic elastic waves in 3D anisotropic media,
    Geophys. J. Int., 191 (2012), pp. 346-366. (PDF. Journal article link)
  4. J. Xia, Y. Xi, and M. Gu, A superfast structured solver for Toeplitz linear systems via randomized sampling,
    SIAM J. Matrix Anal. Appl., 33 (2012), pp. 837-858. (PDF. Journal article link)
  5. S. Li, M. Gu, C. Wu, and J. Xia, New efficient and robust HSS Cholesky Factorization of SPD Matrices,
    SIAM J. Matrix Anal. Appl., 33 (2012), pp. 886-904. (PDF. Journal article link)
  6. J. Xia, A robust inner-outer HSS preconditioner,
    Numer. Linear Algebra Appl., 19 (2012), pp. 992-1016.  (PDF. Journal article link)
  7. J. Xia, On the complexity of some hierarchical structured matrix algorithms,
    SIAM J. Matrix Anal. Appl.    , 33 (2012), pp. 388-410.  (PDF. Journal article link)
  8. W. Shi, X. Wu, and J. Xia, Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations,
    J. Comput. Phys.    , 231 (2012), pp. 7671-7694. (PDF. Journal article link)
  9. S. Wang, J. Xia, M. V. de Hoop, and X. S. Li, Massively parallel structured direct solver for equations describing time-harmonic qP-polarized waves in TTI media,
    Geophys.    , 77 (2012), pp. T69-T82. (PDF. Journal article link)
  10. X. Wu, B. Wang, and J. Xia, Explicit symplectic multidimensional exponential fitting modified Runge-Kutta-Nystr\"om methods,
    BIT Numer. Math., 52 (2012), pp. 773-795. (PDF. Journal article link)
  11. J. Xia, Robust and efficient multifrontal solver for large discretized PDEs,
    High-Perform. Sci. Comput    ., M. W. Berry et al. (eds.), Springer (2012), pp. 199-217. (PDF. Journal article link)
  12. S. Wang, M. V. de Hoop, and J. Xia, On 3D modeling of seismic wave propagation via a structured parallel multifrontal direct Helmholtz solver,
    Geophys. Prospect.    , 59 (2011), pp. 857-873.  (PDF. Journal article link)
  13. J. Xia and M. Gu, Robust approximate Cholesky factorization of rank-structured symmetric positive definite matrices,
    SIAM J. Matrix Anal. Appl., 31 (2010), pp. 2899-2920. (PDF. Journal article link)
  14. J. Xia, S. Chandrasekaran, M. Gu, X. S. Li, Fast algorithms for hierarchically semiseparable matrices,
    Numer. Linear Algebra Appl., 17 (2010), pp. 953-976. (PDF. Journal article link)
  15. S. Wang, M. V. de Hoop, and J. Xia, Acoustic inverse scattering via Helmholtz operator factorization and optimization,
    J. Comput. Phys., 229 (2010), pp. 8445-8462. (PDF. Journal article link)
  16. J. Xia, S. Chandrasekaran, M. Gu, X. S. Li, Superfast multifrontal method for large structured linear systems of equations,
    SIAM J. Matrix Anal. Appl., 31 (2009), pp. 1382-1411. (PDF. Journal article link)
  17. X. Wu, X. You, and J. Xia, Order conditions for ARKN methods solving oscillatory systems,
    Comput. Phys. Commun., 180 (2009), pp. 2250-2257. (PDF. Journal article link)
  18. A. J. Laub and J. Xia, Fast condition estimation for a class of structured eigenvalue problems,
    SIAM J. Matrix Anal. Appl., 30 (2009), pp. 1658-1676. (PDF. Journal article link)
  19. A. J. Laub and J. Xia, Statistical condition estimation for the roots of polynomials,
    SIAM J. Sci. Comput., 31 (2008), pp. 624-643. (PDF. Journal article link)
  20. A. J. Laub and J. Xia, Applications of statistical condition estimation to the solution of linear systems,
    Numer. Linear Algebra Appl., 15 (2008), pp. 489-513. (PDF. Journal article link)
  21. S. Chandrasekaran, M. Gu, J. Xia, and J. Zhu, A fast QR algorithm for companion matrices,
    Oper. Theory Adv. Appl., Birkhauser Basel, 179 (2008), pp. 111-143. (PDF. Journal article link)
  22. S. Chandrasekaran, M. Gu, X. Sun, J. Xia, and J. Zhu, A superfast algorithm for Toeplitz systems of linear equations,
    SIAM J. Matrix Anal. Appl., 29 (2007), pp. 1247-1266. (PDF. Journal article link)
  23. X. S. Li, J. Demmel, L. Grigori, M. Gu, J. Xia, S. Jardin, C. Sovinec, and L.-Q. Lee, Enhancing scalability of sparse direct methods,
    J. Phys.: Conf. Ser., 78 (2007), 012041. (PDF. Journal article link)
  24. X. Wu and J. Xia, Study of general Taylor-like explicit methods in solving stiff ordinary differential equations,
    Int. J. Comput. Math., 84 (2007), pp. 1795-1803.
  25. M. Gu, E. Mengi, M. L. Overton, J. Xia, and J. Zhu, Fast methods for estimating the distance to uncontrollability,
    SIAM J. Matrix Anal. Appl., 28(2) (2006), pp. 477-502. (PDF. Journal article link)
  26. X. Wu and J. Xia, Extended Runge-Kutta-like formulae,
    Appl. Numer. Math., 56 (2006), pp. 1584-1605. (PDF. Journal article link)
  27. X. Wu and J. Xia, Some substantial modifications and improvements for derivative-free iterative methods and derivative-free
    transformation for multiple zeros,
    Appl. Numer. Math., 181 (2006), pp. 1585-1599.
  28. X. Wu, Z. Shen, and J. Xia,An improved regula falsi method with quadratic convergence of both diameter and point
    for enclosing simple zeros of nonlinear equations,
    Appl. Math. Comput., 144 (2003) pp. 381-388.
  29. X. Wu and J. Xia, New vector forms of elementary functions with Taylor series,
    Appl. Math. Comput., 141 (2003) pp. 307-312.
  30. X. Wu and J. Xia, Error analysis of a new transformation for multiple zeros finding free from derivative evaluations,
    Comput. Math. Appl., 46 (2003) pp. 1195-1200.
  31. M. Gu, B. Parlett, D. Ting, and J. Xia, Low-rank update eigensolver for supercell band structure calculations,
    J. Comput. Electron., 1 (2002), pp. 411-414. (PDF. Journal article link)
  32. X. Wu, J. Xia, and F. Yang, A dynamic method for weighted linear squares problems,
    Computing    , 68 (2002) pp. 375-386. (PDF. Journal article link)
  33. X. Wu, J. Xia, and Z. Ouyang, Note on global convergence of ODE method for unconstrained optimization,
    Appl. Math. Comput., 125(2-3) (2002) pp. 311-315.
  34. X. Wu and J. Xia, Two low accuracy methods for stiff systems, with X. Wu,
    Appl. Math. Comput., 123(2) (2001), pp. 141-153.
  35. X. Wu, J. Xia, and R. Shao, Quadratically convergent multiple roots finder method without derivatives,
    Comput. Math. Appl., 42(1-2) (2001) pp. 115-119.
  36. X. Wu and J. Xia, The vector form of a sixth-order A-stable explicit one-step method for stiff problems,
    Comput. Math. Appl., 39(3-4) (2000) pp. 247-257.
  37. X. Wu and J. Xia, An explicit two-step method exact for the scalar test equation y' = \lambda y,
    Comput. Math. Appl., 39(5-6) (2000) pp. 249-257.
  38. X. Wu and J. Xia, A one-step explicit formula for the numerical solution of stiff ordinary differential equation,
    Numer. Math. J. Chinese Univ. (English Ser.), 8 (1999), pp. 53-58.