By directly reciprocating the equations
ax=
h, which appear in numerical integration, structural analysis, etc., the far better first approximate solution
x′=(2
I-
a)
Z′h than those, ever obtained, are nationally found. The ruling retroactive errors in
x′ are then recurrently corrected in series, enabled to converge as fast as possible, in a colum type table. Conventional methods of computation, such as iteration methods, cannot be used generally because considerable errors are actually introduced into the solutions, especially when the coefficients, not situated in the principal diagonal, are large compared to the diagonal ones. Thus, the equations, practically never been solved by the existing methods other than those of elimination, determinants, matrices, etc. up to the present, can perfectly be solved.
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