For the TSQR algorithm, though only one reduce is required throughout the algorithm, the reduction operation is a non-standard one, which corresponds to computing the QR decomposition of a 2nxn matrix formed by concatenating two upper

triangular matrices [5].

Let A = D - L-U, where D is the diagonal matrix and L, U are strictly lower and strictly upper

triangular matrices of A, respectively.

q]) denote the group of unipotent n x n upper

triangular matrices over the q element field [F.

In Section 2 we review the suggested algorithm for finding the inverse of the lower

triangular matrices.

3, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are non-singular lower

triangular matrices with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Let 1 < k [less than or equal to] s < [infinity], A and B be doubly

triangular matrices with A satisfying

For FIML, identical results are obtained for the two equations and

triangular matrices.

Hausdorff matrices were shown by Hurwitz and Silverman [5] to be the class of

triangular matrices that commute with C, the Cesaro matrix of order one.

However, the author anticipates that obtaining the

triangular matrices will increase the complexity and information content thus decreasing the probability of success of completing the analysis.

Let ST(2) be the Lie group of upper

triangular matrices 2x2 with determinant equal to 1 such that the operation of the group is the multiplication between matrices.

The hand-coded version considers the size of M and N and calls specialized routines from the BLAS library to compute the solve operation (\) and the matrix multiplication (N * x) for

triangular matrices.

Second, we develop efficiently implementable variants of guaranteed reliable RRQR algorithms for

triangular matrices originally suggested by Chandrasekaran and Ipsen and by Pan and Tang.