Fast Automatic Differentiation Jacobians by Compact LU Factorization

Fast Automatic Differentiation Jacobians by Compact LU Factorization

For a vector function coded without branches or loops, a code for the Jacobian is generated by interpreting Griewank and Reese’s vertex elimination as Gaussian elimination and implementing this as compact LU factorization. Tests on several platforms show such a code is typically 4 to 20 times faster than that produced by tools such as Adifor, Tamc, or Tapenade, on average significantly faster t...

Fast Ad Jacobians by Compact Lu Factorization

For a vector function, coded without branches or loops, code for the Jacobian is generated by interpreting Griewank and Reese’s Vertex Elimination as Gaussian elimination, and implementing this as compact LU factorization. Tests on several platforms show such code is typically 4 to 20 times faster than that produced by tools such as Adifor, Tamc or Tapenade, on average significantly faster than...

Parallelizing LU Factorization

Systems of linear equations can be represented by matrix equations of the form A~x = ~b. LU Factorization is a method for solving systems in this form by transforming the matrix A into a form that makes backwards and forward susbstitution feasible. A common algorithm for LU factorization is Gaussian elimination, which I used for my serial and parallel implementations. I investigated using async...

Block LU Factorization

Many of the currently popular \block algorithms" are scalar algorithms in which the operations have been grouped and reordered into matrix operations. One genuine block algorithm in practical use is block LU factorization, and this has recently been shown by Demmel and Higham to be unstable in general. It is shown here that block LU factorization is stable if A is block diagonally dominant by c...

LU-AD1 Factorization Algorithm