A Binomial Congruence by Mike Swarbrick Jones

By Mike Swarbrick Jones

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EFI is most suited for the above-mentioned cases. 7. 1). The use of EFI in the solution of power system problems has in practice led to gains in speed, storage, and accuracy that are approximately proportional to the degree of sparsity (Tinney, 1969). 7. Bibliography and Comments The basic Gaussian elimination method and round-off errors are discussed in Fox (1965), Wilkinson (1965), and Forsythe and Moler (1967). The EFI and techniques for keeping it sparse by minimizing the local fill-in have been the subject of extensive attention, for example, Markowitz (1957), Dantzig (1963b), Carpentier (1963), Edelman (1963), Sat0 and Tinney (1963), Tewarson (1967b), Spillers and Hickerson (1968), Brayton et al.

4) = p jz(k). 14) to update Pik) to for all 1 < i < - k + 1 at each stage k. This method avoids the computation of the exact value rik)for each k from the corresponding Bk. 2. Methods Based on A Priori Column Permutatiom time and effort. For large sparse matrices and small values of k, they are reasonably good approximations, but get progressively worse as k increases. Therefore, it is recommended that, if possible, the exact values for rik)sshould be determined from the current B k at periodic intervals.

8) * B)ej = 1, then columns i and j of B belong to the same diagonal block of B. 4)we have B’ * F * B - * ( B * B’)]* B = B’ * [ ( B * B’) * ( B * B’) * * * = (B’ * B ) * (B’ * B) * . . * (B’ * B) = (B’*B)b, Q > v. 1, it follows that ei’(B’ * F * B)ej = ei‘(B’* B y e j = 1 implies that columns i and j are connected by a path and therefore belong to the same diagonal block. This completes the proof of the theorem. 7 for permuting the columns into block diagonal form.

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