• MUMPS

  • Referenced in 504 articles [sw04013]
  • version also available); Iterative refinement and backward error analysis; Various matrix input formats assembled format...
  • SuperLU

  • Referenced in 195 articles [sw00930]
  • condition number, calculate the relative backward error, and estimate error bounds for the refined solutions...
  • MultRoot

  • Referenced in 100 articles [sw00604]
  • outputs the computed roots, multiplicities, backward error, estimated forward error, and the structure-preserving condition...
  • SuperLU-DIST

  • Referenced in 90 articles [sw00002]
  • condition number, calculate the relative backward error, and estimate error bounds for the refined solutions...
  • na10

  • Referenced in 51 articles [sw11511]
  • stop condition, based on a rigorous backward rounding error analysis, guarantees that the computed approximations ... nearby” polynomial. This implies the backward stability of our algorithm. We provide a Fortran...
  • SLRA

  • Referenced in 24 articles [sw11262]
  • polynomials in the weighted 2-norm. Backward error minimization and Sylvester low-rank approximation formulations...
  • FGMRES

  • Referenced in 19 articles [sw04415]
  • criterion is based on a normwise backward error...
  • GMBACK

  • Referenced in 12 articles [sw02139]
  • GMBACK: A generalised minimum backward error algorithm for nonsymmetric linear systems A drawback of employing ... iterative process is that the error must be small if the approximation is accurate. However ... such that the normwise backward error meets some optimality condition...
  • GMRES

  • Referenced in 16 articles [sw00365]
  • criterion is based on a normwise backward error...
  • GSHMC

  • Referenced in 16 articles [sw02631]
  • modified energy is based on backward error results for symplectic time-stepping methods. The proposed...
  • CIMGS

  • Referenced in 12 articles [sw17583]
  • that the CIMGS factorization has better backward error properties than complete Cholesky factorization. For symmetric...
  • GniCodes

  • Referenced in 9 articles [sw21086]
  • understood with the help of a backward error analysis (Section 3). We explain some implications...
  • quadgF

  • Referenced in 5 articles [sw13815]
  • fundamentally different approach to the task – backward error analysis. Other approaches require users to supply...
  • PCOMP

  • Referenced in 21 articles [sw00688]
  • errors, but also hand-coded differentiation. This article introduces the forward and backward accumulation methods...
  • S4NN

  • Referenced in 1 article [sw41327]
  • show how approximated error gradients can be computed backward in a feedforward network with...
  • LMEF

  • Referenced in 3 articles [sw13929]
  • linear multi-step method (explicit, implicit or backward differentiation formulas) with algebraic and/or exponential fitting ... equations. Moreover, LMEF calculates the local truncation error and in the case of exponential fitting...
  • SIMBICON

  • Referenced in 7 articles [sw21525]
  • time, including walking in all directions (forwards, backwards, sideways, turning), running, skipping, and hopping. Controllers ... changes in direction and speed. Feedback-error learning is applied to learn predictive torque models...
  • IJIT

  • Referenced in 1 article [sw21506]
  • algorithm basis, such modifications are laborious and error-prone. In this paper we present ... expansion via image computations, forward or backward. Using our API, we have effortlessly extended various...
  • ADOL-C

  • Referenced in 249 articles [sw00019]
  • ADOL-C: Automatic Differentiation of C/C++. We present...
  • ALBERT

  • Referenced in 82 articles [sw00025]
  • ALBERT - Software for scientific computations and applications. Adaptive...