Solving linear algebraic equations can be interesting
George E. Forsythe · 1952
® Ofi ' (n + l) l * 10 , a number of multiplications which would take the 2 17 3 SWAC some 10 ' years.Actually, only about (l$)h: multiplications 2 , ^National Bureau 'of Standards Western Automatic Computer, an electronic machine easily capable of 2000 multiplications per second.See [6l] for a description, now out of date.f are needed to solve (1); see Bodewig [12], For n 26, (i/^n^* 6000 .and the multiplications would take the SWAC about 3 seconds.It is my hope, on the other hand, to arouse the mathematician's t, interest by showing (section 2) the diversity of approaches to the solution of (l), and by mentioning (sections 3 to 6) some problems associated with selected iterative methods.The newest process on the roster, the method of conjugate gradients, is outlined in section 7. Section 8 touches on the difficult general subject of errors and "condition," while a few words are hazarded in section 9 about the effect of machines on methods.Whether or not the subject proves interesting, the bibliography is intended to make the field look at least respectable l It is a representative condensation of the 5>00-odd titles in the author's file, most of which are in [2y].There are bibliographies on re- lated subjects in Collatz [16] , Dwyer [20], Engineering Research Associates [22], Frame [36], Frankel [37] s Franklin and Hankam [38a],