Secant modification of Newton's method

Dear Bob: Perhaps some of your readers would be interested in knowing that ALGAE I is ready for distribution to interested 704 users. It exists for two 704 configurations, the first of which is the fastest in operation They are: (a) 32K memory, no drums and 6 tapes (including a combined FORTRAN-ALGAE tape, a card-to-tape formed input tape, and an output tape for off-line printing). (b) 8K memory, 4 drums and 7 tapes. It is possible in both systems to perform the compiling with one fe reader. Both systems write their output on an output tape, hence, a later) is required. Dear Mr. Bemer: I am submitting a short note which points out tl Newton's method is frequently faster on a computer by J. H. Wegstein's note on "Accelerating Convert June issue. Although the author does not specificall: tion. I have added a footnote which corrects an er To clarify a matter of convergence which appm Wegstein's note which is superior to the simple iteration (I) x.+1 =f(x.) Denoting the error by ~. =x.-x, where x =f(x), one can show that for smallerrors ~n+1'~"~. • the four eases are obtained as follows: f'(x) <-1 (2)-l<f'(x) < 0 0<f'(x) < 1 l<f'(x) Wegstein this and (