what are computational methods for solving square singular linear system $Ax=0$ for a nonzero $x$ with $A$ of large dimensions?
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Due to roundoff error or noise when constructing $A$, we might find that $A$ numerically has full rank. One approach is to compute the SVD $A = U \Sigma V^T$ and take the singular vector $v_n$, corresponding to the smallest singular value $\sigma_n$, as your null vector. – littleO Jul 21 '14 at 00:52
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Is $A$ sparse? $,$ – Algebraic Pavel Jul 23 '14 at 02:14
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@A is not sparse, but it's symmetric positive definite – user133834 Jul 23 '14 at 16:21
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If the coefficients are floating point then it doesn't make sense for the matrix to be singular, if the coefficients are exact then use some sped-up cousin of Gaussian elimination. – Set May 27 '15 at 20:47