Journal papers:

• N. Halko, P.G. Martinsson, J. Tropp,
  "Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions ".
  Published as arXiv.org report 0909.4061. In review..
  
  
• P. Young and P.G. Martinsson,
  "A Direct Solver for the Rapid Solution of Boundary Integral Equations on Axisymmetric Surfaces in Three Dimensions". In review.
  
  
• L. Greengard, D. Gueyffier, P.G. Martinsson, V. Rokhlin,
  "Fast direct solvers for integral equations in complex three-dimensional domains".
  Acta Numerica, 18, pp. 243-275, 2009.
  
  
• Edo Liberty, Franco Woolfe, Per-Gunnar Martinsson, Vladimir Rokhlin, and Mark Tygert,
  "Randomized algorithms for the low-rank approximation of matrices".
  Proceedings of the National Academy of Sciences 2007 104: 20167-20172.
  
  
• P.G. Martinsson,
  "A fast direct solver for a class of elliptic partial differential equations"
  Journal of Scientific Computation, pp.~316-330, 38(3), 2009.
  
  
• P.G. Martinsson, G.J.Rodin
  "Boundary Algebraic Equations for Lattice Problems"
  Proceedings of the Royal Society A, 465(2108), pp. 2489-2503, 2009.
  
  
• P.G. Martinsson, V. Rokhlin, and M. Tygert,
  "A randomized algorithm for the approximation of matrices".
  In review. Yale CS research report YALEU/DCS/RR-1361.
  
  
• P.G. Martinsson, V. Rokhlin, and M. Tygert,
  "On interpolation and integration in finite-dimensional spaces of bounded functions".
  Communications in Applied Mathematics and Computational Science, 1, Jan. 2006. (Local copy.)
  
  
• P.G. Martinsson and V. Rokhlin,
  "A fast direct solver for scattering problems involving elongated structures".
  Journal of Computational Physics, 221, pp. 288 - 302, 2007.
  
  
• P.G. Martinsson and V. Rokhlin,
  "An accelerated kernel-independent fast multipole method in one dimension" .
  SIAM Journal of Scientific Computing, 29(3), pp. 1160-1178, 2007.
  

• P.G. Martinsson,
  "Rapid evaluation of electro-static interactions in multi-phase dielectric media".
  Journal of Computational Physics, 211, pp. 289 - 299, 2006.
  
  
• P.G. Martinsson, V. Rokhlin, M. Tygert
  "A fast algorithm for the inversion of general Toeplitz matrices".
  Computers and Mathematics with Applications, 50(5), pp 741 - 752, 2005.
  
  
• P.G. Martinsson and V. Rokhlin
  "A fast direct solver for boundary integral equations in two dimensions".
  Journal of Computational Physics, 205(1), pp. 1-23, 2005.
  
  
• H. Cheng, Z. Gimbutas, P.G. Martinsson, V. Rokhlin,
  "On the compression of low rank matrices".
  SIAM Journal of Scientific Computing, 26(4), pp. 1389-1404, 2005. Clarifications / corrections.
  
  
• P.G. Martinsson and I. Babuska,
  "Mechanics of materials with periodic truss or frame micro-structures".
  Archives of Rational Mechanics and Analysis, 185(2), pp. 201-234, 2007.
  
  
• P.G. Martinsson and I. Babuska,
  "Homogenization of materials with periodic truss or frame micro-structures".
  Mathematical Models and Methods in Applied Sciences, 17(5), pp. 805-832, 2007.
  
  
• P.G. Martinsson and G. Rodin,
  "Boundary algebraic equations for lattice problems".
  IUTAM proceedings, Liverpool, 2002.
  
  
• P.G. Martinsson and G. Rodin,
  "Asymptotic expansions of lattice Green's functions".
  Proceedings of the Royal Society A , 458 , 2002, pp. 2609--2622.
  
  
• P.G. Martinsson and A.B. Movchan,
  "Vibrations of lattice structures and phononic bandgaps".
  The Quarterly Journal of Mechanics and Applied Mathematics , 56 , 2003, pp. 45-64.
  
  
• E. Cornea, R. Howard and P.G. Martinsson,
  "Solutions near singular points to the Eikonal and related first-order nonlinear partial differential equations in two dimensions".
  Differential and Integral Equations , 14 , 2001, pp. 1441-1468.
  

Theses:

• P.G. Martinsson, (under the supervision of Professors Ivo Babuska and Gregory Rodin)
  "Fast Multiscale Methods for Lattice Equations".
  Doctoral Thesis, Computational and Applied Mathematics, University of Texas at Austin, June 2002.
  
  
• P.G. Martinsson, (under the supervision of Professor Vidar Thomee)
  "Discretisation of Certain Evolution Equations with Memory using Convolution Quadrature".
  Licentiate Thesis, Dept. of Mathematics, Chalmers University of Technology, 1998.
  
  
• P.G. Martinsson, (under the supervision of Dr William McLean)
  "Separation of Variables Techniques in Particle Simulations and Integral Equations".
  Honours Thesis, Dept. of Mathematics, University of New South Wales, 1995.