Publications and Preprints

Submitted/Preprints
  1. J. Xia, Multi-layer hierarchical structures and factorizations, SIAM J. Matrix Anal. Appl., submitted, 2016, Purdue CCAM Report CCAM-2016-6. (PDF)
  2. J. Xia and Z. Xin, Effective and robust preconditioning of general SPD matrices via structured incomplete factorization, submitted, 2017, Purdue CCAM Report CCAM-2017-1. (PDF)
  3. J. Shen, Y. Wang, and J. Xia, Fast Structured Jacobi-Jacobi Transforms, submitted, 2017.
  4. J. Xia, Matrix-free sparse direct solvers, preprint.
  5. D. Cai and J. Xia, Bridging the gap between the fast multipole method and fast stable structured factorizations, preprint.
  6. J. Vogel, J. Xia, Z. Xin, S. Cauley, and V. Balakrishnan, Superfast divide-and-conquer eigenvalue decompositions: revisited, to be submitted, (2016).
  7. Superfast sparse arbitrary inversion, with X. Liu, Y. Xi, and M. de Hoop, preprint.
  8. A multi-structured superfast and stable Toeplitz solver, with M. Gu, preprint.
  9. O(n) complexity randomized 3D direct solver with MHS structure, Purdue GMIG Report 14-18, April 2014.
  10. Fast structured solvers for finding the eigenvalues of large structured matrices, with Y. Xi, preprint.
  11. Robust symmetric SPIKE algorithm for large banded SPD matrices, preprint.
Papers  (Google Scholar Citations. PDF files for personal use only. Copyright: journals)
  1. X. Ye, J. Xia, R. Chan, S. Cauley, and V. Balakrishnan, A fast contour-integral eigensolver for non-Hermitian matrices,
    SIAM J. Matrix Anal. Appl.
    , to appear, (2017) (PDF. Journal article link)
  2. Z. Xin, J. Xia, M. V. de Hoop, S. Cauley, and V. Balakrishnan, A distributed-memory randomized structured multifrontal method for sparse direct solutions,
    SIAM J. Sci. Comput., to appear, (2017) (PDF. Journal article link)
  3. Y. Xi and J. Xia, On the stability of some hierarchical rank structured matrix algorithms,
    SIAM J. Matrix Anal. Appl., 37 (2016), pp. 1279-1303. (PDF. Journal article link)
  4. J. Vogel, J. Xia, S. Cauley, and V. Balakrishnan, Superfast divide-and-conquer method and perturbation analysis for structured eigenvalue solutions,
    SIAM J. Sci. Comput.
    , 38 (2016), pp. A1358-A1382. (PDF. Journal article link)
  5. X. Liu, J. Xia, and M. V. de Hoop, Parallel randomized and matrix-free direct solvers for large structured dense linear systems,
    SIAM J. Sci. Comput., 38 (2016), S508-S538. (PDF. Journal article link)
  6. S. Wang. X. S. Li, F. H. Rouet, J. Xia, and M. V. de Hoop, A parallel geometric multifrontal solver using hierarchically semiseparable structure,
    ACM Trans. Math. Software, 42 (2016), Article 21. (PDF. Journal article link)
  7. D. J. Hardy, M. A. Wolff, J. Xia, K. Schulten, and R. D. Skeel, Multilevel summation with B-spline interpolation for pairwise interactions in molecular dynamics simulations,
    J. Chem. Phys., 144 (2016), 114112. (PDF. Journal article link)
  8. J. Shen, Y. Wang, and J. Xia, Fast structured direct spectral methods for differential equations with variable coefficients, I. The one-dimensional case,
    SIAM J. Sci. Comput., 38 (2016), pp. A28-A54. (PDF--erratum. Journal article link)
  9. J. Xia, Z. Li, and X. Ye, Effective matrix-free preconditioning for the augmented immersed interface method,
    J. Comput. Phys., 303 (2015), pp. 295-312. (PDF. Journal article link)
  10. J. Xia, Y. Xi, S. Cauley, and V. Balakrishnan, Fast sparse selected inversion,
    SIAM J. Matrix Anal. Appl., 36 (2015), pp. 1283-1314. (PDF. Journal article link)
  11. S. Cauley, Y. Xi, B. Bilgic, J. Xia, E. Adalsteinsson, V. Balakrishnan, L. Wald, and K. Setsompop, Fast reconstruction for multi-channel compressed sensing using a hierarchically semiseparable solver,
    Magn. Reson. Med., 73 (2015), pp. 1034-1040. (PDF. Journal article link)
  12. Y. Xi, J. Xia, and R. Chan, A fast randomized eigensolver with structured LDL factorization update,
    SIAM J. Matrix Anal. Appl., 35 (2014), pp. 974-996. (PDF. Journal article link)
  13. Y. Xi, J. Xia, S. Cauley, and V. Balakrishnan, Superfast and stable structured solvers for Toeplitz least squares via randomized sampling,
    SIAM J. Matrix Anal. Appl.
    , 35 (2014), pp. 44-72. (PDF. Journal article link)
  14. S. Wang, X. S. Li, J. Xia, Y. Situ, and M. V. de Hoop, Efficient scalable algorithms for solving dense linear systems with hierarchically semiseparable structures,
    SIAM J. Sci. Comput., 35 (2013), C519-C544. (PDF. Journal article link)
  15. B. Wang, X. Wu, and J. Xia, Error bounds for explicit ERKN integrators for systems of multi-frequency oscillatory second-order differential equations,
    Appl. Numer. Math., 74 (2013), pp. 17-34. (PDF. Journal article link)
  16. J. Xia, Randomized sparse direct solvers,
    SIAM J. Matrix Anal. Appl., 34 (2013), pp. 197-227. (PDF. Journal article link--Fig. 3.3)
  17. J. Xia, Efficient structured multifrontal factorization for general large sparse matrices,
    SIAM J. Sci. Comput., 35 (2013), pp. A832-A860. (PDF. Journal article link)
  18. 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)
  19. 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)
  20. 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)
  21. J. Xia, A robust inner-outer HSS preconditioner,
    Numer. Linear Algebra Appl., 19 (2012), pp. 992-1016.  (PDF. Journal article link)
  22. 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)
  23. 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)
  24. 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)
  25. 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)
  26. 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)
  27. 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)
  28. 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)
  29. 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)
  30. 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)
  31. 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)
  32. 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)
  33. 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)
  34. 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)
  35. 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)
  36. 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)

  37. 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)
  38. 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)
  39. 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.
  40. 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)
  41. X. Wu and J. Xia, Extended Runge-Kutta-like formulae,
    Appl. Numer. Math., 56 (2006), pp. 1584-1605. (PDF. Journal article link)
  42. 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.
  43. 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.
  44. X. Wu and J. Xia, New vector forms of elementary functions with Taylor series,
    Appl. Math. Comput., 141 (2003) pp. 307-312.
  45. 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.
  46. 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)
  47. 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)
  48. 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.

  49. X. Wu and J. Xia, Two low accuracy methods for stiff systems, with X. Wu,
    Appl. Math. Comput., 123(2) (2001), pp. 141-153.

  50. 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.

  51. 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.

  52. 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.

  53. 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.