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r=invupdt(a,x,w);where R is an n ×w matrix; A is an n ×n positive definite matrix; X is an n ×1 or 1 ×n vector; and w is an optional scalar (if not specified, w has default value 1).
r=a-w*a*x*inv(1+w*x`*a*x)*x`*a;The INVUPDT function is used primarily to update a matrix inverse because the function has the property
c2=invupdt(c,x);where C = INV(Z'Z). Note that
c2=inv((z//x)`*(z//x));If w is 1, the function adds an observation to the inverse; if w is -1, the function removes an observation from the inverse. If weighting is used, w is the weight.
To perform the computation, the INVUPDT function uses about 2n^{2} multiplications and additions, where n is the row dimension of the positive definite argument matrix.
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