Given a symmetric matrix L, and the inverse of L is difficult to solve. Is there any other way to calculate the sum( inverse(L)(:,i) ) ?
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Why do you require that result? – Oliver Charlesworth Jan 26 '15 at 00:40
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The matrix is always high dimensional, i do not need the whole inverse matrix, just the column sum of the inverse matrix, so i want to find a method to calculate it quickly! – Alex Jan 26 '15 at 00:43
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It can be shown that
sum ( inverse(L)(:,i) ) = x(i)
where the vector x is the solution to the simultaneous equations
L x = (1,1,...,1)'
(' denotes transposition). Since solving a system of linear equations is much faster than inverting a matrix (O(n²) vs O(n log(n))), this should improve the speed of the computation.
Gregor de Cillia
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