Re: CPU time for Solve under v.2.0 and 2.1

• To: mathgroup at yoda.physics.unc.edu
• Subject: Re: CPU time for Solve under v.2.0 and 2.1
• From: withoff
• Date: Mon, 16 Nov 92 16:40:19 CST

```> Dear mma users,
>
> here's an example of strange v.2.1 behavior when I try to solve
> a matrix equation using the Solve command on my Mac IIci + a Tokamac 68040
> board.
>
> As we see, the same program below gives very different CPU time !!!
> A bad part is that the v.2.1 gives 5 times longer CPU time !!!!!
>
> Any comments are really welcome.
>
> Kiyoshi Yoda

The algorithm for solving systems of symbolic linear equations was
changed between V2.0 and V2.1.  In most cases the change seems to
be for the better, sometimes dramatically so, but there are obviously
cases for which it is not.  Here are some typical examples in which
the V2.1 algorithm is better:

-----------------------------------------------------------
Version 2.1:

In[2]:= LinearSolve[{{a, b, -a, 0, b},
{a, 0, b, -c, 0},
{0, b, -a, c, 0},
{a, b, -c, 0, 0},
{0, 0, 0, -b, 0}}, {0,0,0,0,1}]; //Timing

Out[2]= {0.2 Second, Null}

In[3]:= LinearSolve[{{a1,0,a3,a4},
{b1,0,b3,b4},
{c1,0,c3,c4}}, {x, y, z}]; //Timing

Out[3]= {0.1 Second, Null}

--------------------------------------------------------------
Version 2.0

In[1]:= LinearSolve[{{a, b, -a, 0, b},
{a, 0, b, -c, 0},
{0, b, -a, c, 0},
{a, b, -c, 0, 0},
{0, 0, 0, -b, 0}}, {0,0,0,0,1}]; //Timing

Out[1]= {0.333333 Second, Null}

In[2]:= LinearSolve[{{a1,0,a3,a4},
{b1,0,b3,b4},
{c1,0,c3,c4}}, {x, y, z}]; //Timing

Out[2]= {3.53333 Second, Null}

--------------------------------------------------------------

The speed degradation problem is obviously soluble, if by no other method
then by simply including both algorithms.  This problem will be addressed
in an upcoming release.

Dave Withoff
withoff at wri.com

```

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