《数值分析》课程教学资源（课外阅读）Is Numerical Analysis Boring（Sullivan, 2006）

THE LAST WORD IS NUMERICAL ANALYSIS BORING? N PRINCIPLE,THIS COULD BE A FOUR-WORD ESSAY BECAUSE THE SHORT AN. SWER IS,"NO,OF COURSE NOT!"INDEED,MY ASKING THE QUESTION ENTAILS A SLIGHT PERSONAL RISK:I CERTAINLY DONT WANTTO ALIENATE MY FRIENDS WHO ARE NUMERICAL ANALYSTS.I'VE WORKED HAPPILY,IF NOT EXACTLY IN. peptlpa1onghitoyotgketitgogtpeopkob Instead of annoying the numerical analysis comm nity, computa sts ext vsts have themselves recently asked whether their subiect why its practition no.16;www.netl .org/r ges don,using un complained that the Digest was becomir dull and sug- i油n3品 I by its The first le,wecigtecnnoticeinterestinglimiationsofsa r po e rather than use professional code based on well suffer fror ho tatus and I'm just not aware of it.How r ha tools such as Mathematica and Matlab offer explorers the using very ing41do间 ds. users might ll combine me d parts of ma ler the hoc merical analysis,but first we must analysis actually is.For now,let's say that it's primarily the when the teacher enters the room,jump upand down and olished by the IEEE CS and the Al 15219615/06/520.0002006▣

104 Copublished by the IEEE CS and the AIP 1521-9615/06/$20.00 © 2006 IEEE COMPUTING IN SCIENCE & ENGINEERING T HE L AST W ORD then certainly someplace near, the field of numerical analy￾sis for many years. I’ve even taught it (not a guarantee against being boring, I know) and coauthored a book on one of the field’s many active subareas. Instead of annoying the numerical analysis community, I want to comment on the fact that a few numerical ana￾lysts have themselves recently asked whether their subject is boring. It all began with a posting to NA Digest (vol. 6, no. 16; www.netlib.org/na-digest-html/06/v06n16.html) by one of the field’s most distinguished researchers. He complained that the Digest was becoming dull and sug￾gested that some controversial posts might liven things up. Well, his initial post certainly did so all by itself. The first response claimed that not only is NA Digest dull, but some very important topics in numerical analysis have also be￾come dull—nothing new or exciting is happening, at least in that poster’s opinion. Later posts claimed that cliques tend to dominate some meetings of numerical analysts and discuss problems of merely academic interest while ne￾glecting real-world applications. Perhaps workers in other scientific fields suffer from sim￾ilar episodes of anguish and self-doubt about the subject’s status and I’m just not aware of it. However, having for many years heard complaints against numerical analysis by numerical analysts citing “dullness” and “irrelevance for solving the real problems,” I doubt that the suffering in other fields is quite the same as it is here (always excepting, of course, certain profound but arcane specialties in certain not-to-be-named parts of mathematics). I can offer plausible reasons for the special case of nu￾merical analysis, but first we must agree on what numerical analysis actually is. For now, let’s say that it’s primarily the science of getting the correct answer to numerical compu￾tations. Secondarily, it deals with getting the correct answer efficiently and explaining why the answer is correct as well as how correct it is as a function of the amount of effort ex￾pended on performing the computation. Perhaps a long history of struggle trying to get people to do computations correctly leaves numerical analysts extra con￾cerned about how others perceive the field. I’m certain that the history of numerical analysis explains why its practition￾ers are so touchy about the idea of initiating a computation in a spirit of wild abandon, using untested and unanalyzed folk methods, paying no attention at all to rigor or correctness. But many people have a natural desire to fool around with computations. We like to explore and experiment. If we’re alert, we might even notice interesting limitations of stan￾dard numerical methods. Occasionally, naïve experimenta￾tion helps us discover new things or rediscover old things in new settings. Some might even say that too much rigor too early chokes off interesting ideas and stifles creativity. On the other hand, I don’t really think we should en￾courage those who want to “roll their own” numerical software rather than use professional code based on well￾analyzed methods. After all, who wants to fly on a plane de￾signed with home-crafted numerical methods? Fortunately, tools such as Mathematica and Matlab offer explorers the possibility of doing lots of experiments while using very good methods. Naturally, users might still combine meth￾ods in strange ways, but when strange things happen, they probably won’t be due to the underlying components. Those who want to know about the interesting things un￾der the hood of packages like Mathematica and Matlab re￾ally ought to take a course in numerical analysis—while you’re at it, leave an apple on the teacher’s desk. Better yet, when the teacher enters the room, jump up and down and scream and dance in the aisles, like you’re in the audience at a Rolling Stones concert. IS NUMERICAL ANALYSIS BORING? By Francis Sullivan I N PRINCIPLE, THIS COULD BE A FOUR-WORD ESSAY BECAUSE THE SHORT AN￾SWER IS, “NO, OF COURSE NOT!” INDEED, MY ASKING THE QUESTION ENTAILS A SLIGHT PERSONAL RISK: I CERTAINLY DON’T WANT TO ALIENATE MY FRIENDS WHO ARE NUMERICAL ANALYSTS. I’VE WORKED HAPPILY, IF NOT EXACTLY IN, Authorized licensed use limited to: East China Normal University. Downloaded on January 20, 2009 at 03:32 from IEEE Xplore. Restrictions apply