Hi,

I'm trying to invert a 25x25 sparse symbolic matrix, which for concreteness I've included below. I have tried

Inverse[A,Method->OneStepRowReduction]

but it's still running after an hour (8-core 2.6GHz Intel Xeon Mac, 32Gb memory). Same with Method->Automatic. I know I could be more patient and give it a day or two, but even an hour seems on the long side, given that the matrix is mostly zeroes. I realize this is a question that has probably been asked before but I haven't been able to find a good answer or even a systematic strategy, including in the posts on other web forums that I found. So I apologize if it's a redundant question. With that said, does anyone have any thoughts?

Thanks!

Ian

A = {{1, -b1, 0, 0, 0, -b2, 0, 0, 0, 0, 0, 0, -c1, 0, 0, 0, 0, 0, -c2, 0, 
  0, 0, 0, 0, 0}, {0, 1 - g11, 0, 0, 0, -g12, 0, 0, 0, 0, 0, 0, -h11, 
  0, 0, 0, 0, 0, -h12, 0, 0, 0, 0, 0, 0}, {0, b1 (-1 + x1), 1 - x1, 0,
   0, b2 (-1 + x1), 0, 0, 0, 0, 0, 0, 0, -c1, 0, 0, 0, 0, 0, -c2, 0, 
  0, 0, 0, 0}, {0, g11 (-1 + x1), 0, 1 - x1, 0, g12 (-1 + x1), 0, 0, 
  0, 0, 0, 0, 0, -h11, 0, 0, 0, 0, 0, -h12, 0, 0, 0, 0, 0}, {0, 
  g21 (-1 + x1), 0, 0, 1 - x1, g22 (-1 + x1), 0, 0, 0, 0, 0, 0, 
  0, -h21, 0, 0, 0, 0, 0, -h22, 0, 0, 0, 0, 0}, {0, -g21, 0, 0, 0, 
  1 - g22, 0, 0, 0, 0, 0, 0, -h21, 0, 0, 0, 0, 0, -h22, 0, 0, 0, 0, 0,
   0}, {0, b1 (-1 + x2), 0, 0, 0, b2 (-1 + x2), 1 - x2, 0, 0, 0, 0, 0,
   0, 0, -c1, 0, 0, 0, 0, 0, -c2, 0, 0, 0, 0}, {0, g11 (-1 + x2), 0, 
  0, 0, g12 (-1 + x2), 0, 1 - x2, 0, 0, 0, 0, 0, 0, -h11, 0, 0, 0, 0, 
  0, -h12, 0, 0, 0, 0}, {0, g21 (-1 + x2), 0, 0, 0, g22 (-1 + x2), 0, 
  0, 1 - x2, 0, 0, 0, 0, 0, -h21, 0, 0, 0, 0, 0, -h22, 0, 0, 0, 
  0}, {0, b1 (-1 + y1), 0, 0, 0, b2 (-1 + y1), 0, 0, 0, 
  1 - a y1, -c1, -c2, 0, 0, 0, 0, -c2, 0, 0, 0, 0, -b1 y1, 0, -b2 y1, 
  0}, {0, q11 (-1 + y1), 0, 0, 0, q12 (-1 + y1), 0, 0, 0, -p1 y1, 
  1 - r11, -r12, 0, 0, 0, 0, -r12, 0, 0, 0, 0, -q11 y1, 0, -q12 y1, 
  0}, {0, q21 (-1 + y1), 0, 0, 0, q22 (-1 + y1), 0, 0, 
  0, -p2 y1, -r21, 1 - r22, 0, 0, 0, 0, -r22, 0, 0, 0, 0, -q21 y1, 
  0, -q22 y1, 0}, {0, -q11, 0, 0, 0, -q12, 0, 0, 0, 0, 0, 0, 1 - r11, 
  0, 0, 0, 0, 0, -r12, 0, 0, 0, 0, 0, 0}, {0, q11 (-1 + x1), 0, 0, 0, 
  q12 (-1 + x1), 0, 0, 0, 0, 0, 0, 0, 1 - r11, 0, 0, 0, 0, 0, -r12, 0,
   0, 0, 0, 0}, {0, q11 (-1 + x2), 0, 0, 0, q12 (-1 + x2), 0, 0, 0, 0,
   0, 0, 0, 0, 1 - r11, 0, 0, 0, 0, 0, -r12, 0, 0, 0, 0}, {0, 
  b1 (-1 + y2), 0, 0, 0, b2 (-1 + y2), 0, 0, 0, 0, 0, 0, 0, 0, 0, 
  1 - a y2, 0, -c2, 0, 0, 0, 0, -b1 y2, 0, -b2 y2}, {0, q21 (-1 + y1),
   0, 0, 0, q22 (-1 + y1), 0, 0, 0, -p2 y1, -r21, -r22, 0, 0, 0, 0, 
  1 - r22, 0, 0, 0, 0, -q21 y1, 0, -q22 y1, 0}, {0, q21 (-1 + y2), 0, 
  0, 0, q22 (-1 + y2), 0, 0, 0, 0, 0, 0, 0, 0, 0, -p2 y2, 0, 1 - r22, 
  0, 0, 0, 0, -q21 y2, 0, -q22 y2}, {0, -q21, 0, 0, 0, -q22, 0, 0, 0, 
  0, 0, 0, -r21, 0, 0, 0, 0, 0, 1 - r22, 0, 0, 0, 0, 0, 0}, {0, 
  q21 (-1 + x1), 0, 0, 0, q22 (-1 + x1), 0, 0, 0, 0, 0, 0, 0, -r21, 0,
   0, 0, 0, 0, 1 - r22, 0, 0, 0, 0, 0}, {0, q21 (-1 + x2), 0, 0, 0, 
  q22 (-1 + x2), 0, 0, 0, 0, 0, 0, 0, 0, -r21, 0, 0, 0, 0, 0, 1 - r22,
   0, 0, 0, 0}, {0, g11 (-1 + y1), 0, 0, 0, g12 (-1 + y1), 0, 0, 
  0, -f1 y1, -h11, -h12, 0, 0, 0, 0, -h12, 0, 0, 0, 0, 1 - g11 y1, 
  0, -g12 y1, 0}, {0, g11 (-1 + y2), 0, 0, 0, g12 (-1 + y2), 0, 0, 0, 
  0, 0, 0, 0, 0, 0, -f1 y2, 0, -h12, 0, 0, 0, 0, 1 - g11 y2, 
  0, -g12 y2}, {0, g21 (-1 + y1), 0, 0, 0, g22 (-1 + y1), 0, 0, 
  0, -f2 y1, -h21, -h22, 0, 0, 0, 0, -h22, 0, 0, 0, 0, -g21 y1, 0, 
  1 - g22 y1, 0}, {0, g21 (-1 + y2), 0, 0, 0, g22 (-1 + y2), 0, 0, 0, 
  0, 0, 0, 0, 0, 0, -f2 y2, 0, -h22, 0, 0, 0, 0, -g21 y2, 0, 
  1 - g22 y2}}