<html><head><meta http-equiv="Content-Type" content="text/html charset=windows-1252"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><br><div><div>On 12 Jul 2016, at 10:23, Michael Clark <<a href="mailto:michael.clark@gatech.edu">michael.clark@gatech.edu</a>> wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div dir="ltr"><div><div><div><div><div>Hello,<br><br></div>I have a system of equations for time derivatives of the form A(udot) = b, where A is a symmetric matrix, udot is a vector of time derivatives to solve for, and b is a vector of right-hand sides.<br><br></div>I'd like to compute the udot vector using Kranc, as the vector b involves a great deal of tensor math that I would like to use TensorTools for.<br><br></div>What options do I have to solve this problem?<br><br>In particular, the form of the matrix A does not change in time--only the values of its nonzero entries would vary. If it could be factored or inverted symbolically so that the time-varying quantities could be input to it at each step, I think that would be ideal, rather than running a full matrix-inversion or factorization at every step.<br></div></div></div></blockquote><div><br></div><div>Hi Michael,</div><div><br></div><div>A few questions:</div><div><br></div><div>– Is this a linear system, so that A(udot) = A . udot, or is A a general matrix-valued function of udot?</div><div><br></div><div>– How large is the matrix A?</div><div><br></div><div>– If you have a general symbolic form for A, can you compute its inverse in Mathematica, or is it too complicated?</div></div><br><div apple-content-edited="true">
<div style="color: rgb(0, 0, 0); letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div style="color: rgb(0, 0, 0); letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div style="color: rgb(0, 0, 0); letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div style="color: rgb(0, 0, 0); letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div>-- </div><div>Ian Hinder</div><div><a href="http://members.aei.mpg.de/ianhin">http://members.aei.mpg.de/ianhin</a></div></div></div></div></div>
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