The authors study the finite arithmetic properties of the Schur and the lattice recursions. They derive the error variance of the reflection coefficient at each stage of each algorithm and present experimental results which agree very closely with the analytical results. They also show that the lattice recursions have a significant accuracy advantage over the Schur recursions when the problem is ill-conditioned or, equivalently, when the absolute values of the reflection coefficients are close to one. >
The authors introduce a fast algorithm for computing the QR factors of a complex vertically circulant matrix C. The complexity of the algorithm is 5mn+2n/sup 2/+O(m) complex-fixed point operations or 3mn+n/sup 2/+O(m) complex floating-point operations, where m is the number of rows in C and n is the number of columns (it is supposed that m >
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.