• 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...