Technical Report CS0013

Authors: N. Katz· and E. Kantorowitz
Abstract: In an experimental study [4], Rice compared 3 algorithms for the generation of a set of orthogonal vectors which is equivalent to a given set of vectors. For function-generated vecotrs., which correspond to most applications. the modified Gram-Schmidt(MGS) procedure produced consistently more accurate results than the classical Gram-Schmidt method. The study is continued here and 3 new procedures, the first-order correction(FOC), the modified first-order correction (MFOC), and the modified single reinforcement (MSR). are introduced. The experiments indicate that the accuracies obtained by the MGS. FOC, and MFOC methods are of the same magnitude of order. Since the MGS algorithm involves the smallest amount of arithmetic operations and of computer storage. it may be recommended in the "normal" case. MSR reqUires about twice as many operations as MGS. but is numerically considerably "stronger" and may, therefore. be recommended in "nearly pathological" cases.
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