Lists of equations. Again

*To*: mathgroup at smc.vnet.net*Subject*: [mg56274] Lists of equations. Again*From*: Maxim <ab_def at prontomail.com>*Date*: Wed, 20 Apr 2005 05:32:50 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

In version 5.0 FindRoot[{{x, y} == {1, 1}}, {x, 2}, {y, 2}] failed: it complained about the non-numerical jacobian and just returned the starting point. This now works in version 5.1; however, there is still exactly the same problem with higher-dimensional lists: FindRoot[Array[a, {2, 2}] == IdentityMatrix[2], Evaluate[Sequence@@ (Flatten[#, 1]&)@ Array[{a[##], 0}&, {2, 2}]]] This generates Thread::tdlen and FindRoot::njnum messages, indicating that there is again something wrong with the processing of lists. Strangely, FindRoot[Array[a, {2, 2}] - IdentityMatrix[2], Evaluate[Sequence@@ (Flatten[#, 1]&)@ Array[{a[##], 0}&, {2, 2}]]] works without a problem (another possible way to resolve this issue is to specify Jacobian -> IdentityMatrix[4]). If the specified form of the jacobian doesn't have the correct structure, this often results in the kernel crash: FindRoot[x == {1, 2}, {x, {0, 0}}, Jacobian -> {{{1}, {1}}}] (*crashes the kernel*) This may happen even if the structure is correct: FindMinimum[x^2, {x, 1}, Method -> {Newton, Hessian -> {{2}}}] (*crashes the kernel*) Here the hessian is specified correctly, but unless the gradient is also given explicitly as Gradient -> {2x}, all the other settings (Automatic, Symbolic, FiniteDifference) lead to the kernel crash. Maxim Rytin m.r at inbox.ru