Experiments on Gram-Schmidt orthogonalization
John R. Rice · Mathematics of Computation · 1966
The present paper contains in Table 1 a somewhat shortened version of that summary, and lists all values of | k \ for which six or more solutions were found.We summarize some of our results as follows:(1) For positive k g 100, no solution could be appended to the Table in [3].(2) For negative k 2ï -9999, the last solution found was(1,775,104)3 -(2,365,024,826)2 = -5412;whilst, for positive fc ^ 9999, the last solution was(939,787)3 -(911,054,064)2 = 307.(3) In addition to solutions for | k | ^ 9999, we have solutions, for y ^ 104and | k | g 99999; there are 1221 for positive k and 799 for negative k.The vast majority of solutions are with y < 100 and Table 2 gives the number of solutions for various ranges of y.The fact that the number of solutions is a rapidly decreasing function of y suggests that for at least some k the solution set may be complete.