67:
49:
77:
22:
188:
quadratic factor has distinct or identical roots, as it is searching for the quadratic coefficients, and not for the roots directly. I've never seen a reference which stated the latter specifically, but there is lots of literature on the quadratic multiplicity difficulty, and one would conjecture that if double roots also caused a problem, they would be mentioned in that.
187:
Bairstow's method loses its quadratic rate of convergence when trying to find a quadratic factor of multiplicity greater than one, although there are a couple of modifications to it which fix this. I do not believe it loses its quadratic convergence to a single quadratic factor based on whether that
300:
In the section "Example", it says 'the method produced a quadratic factor that contains the roots -1/3 and -3'. I have checked that this method does indeed produce these roots for this example. It's not obvious from the table that these are the roots.
171:
Is the method really quadratically convergent, even in the case of double roots, as the article implies? Do you have a reference for this? I would guess that it is only linearly convergent in this case, just as Newton's method. Cheers,
204:"Like Newton's Method, Bairstow's Algorithm will converge quadratically providing the initial guess is close enough to the zero. The algorithm can be quite slow to converge to quadratic factors of multiplicity higher than 1."
209:
I read this as saying that the algorithm will also converge quadratically, albeit slowly, in the case of quadratic factors of multiplicity higher than one. What do you think about reformulating this as
240:
I intended the comment about multiplicity to be an exception to the first line about quadratic convergence. You are correct that this is less than clear. Your suggested phrasing is fine.
213:"Bairstow's algorithm inherits the quadratic convergence of Newton's method, except in the case of quadratic factors of multiplicity higher than 1, when convergence can be rather slow.."
269:
for future reference. I hope that you continue to contribute to
Knowledge; you clearly know this stuff and it is essential for Knowledge to attract more experts. Cheers,
336:
123:
129:
331:
99:
308:
90:
54:
29:
312:
274:
223:
177:
161:
35:
304:
201:
I was refering to the case of a quadratic factor of multiplicity greater than one. The article says
153:
98:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
262:
270:
219:
173:
157:
66:
48:
241:
189:
181:
165:
82:
325:
76:
316:
278:
244:
227:
192:
72:
95:
15:
94:, a collaborative effort to improve the coverage of
28:This article has not yet been rated on Knowledge's
128:This article has not yet received a rating on the
265:as indicated above, and copied this section to
8:
43:
21:
19:
45:
261:Thank you for your answer. I changed
7:
88:This article is within the scope of
337:Unknown-importance science articles
34:It is of interest to the following
14:
147:Convergence of Bairstow's method
75:
65:
47:
20:
1:
108:Knowledge:WikiProject Science
102:and see a list of open tasks.
317:17:19, 7 November 2011 (UTC)
279:15:11, 14 January 2006 (UTC)
245:05:05, 14 January 2006 (UTC)
228:03:47, 14 January 2006 (UTC)
193:02:44, 14 January 2006 (UTC)
182:23:00, 13 January 2006 (UTC)
166:15:11, 14 January 2006 (UTC)
111:Template:WikiProject Science
332:Unassessed science articles
218:or something similar. --
353:
130:project's importance scale
127:
60:
42:
267:Talk:Bairstow's method
146:
154:User talk:Hermitian
91:WikiProject Science
30:content assessment
307:comment added by
263:Bairstow's method
144:
143:
140:
139:
136:
135:
344:
319:
116:
115:
114:science articles
112:
109:
106:
85:
80:
79:
69:
62:
61:
51:
44:
25:
24:
23:
16:
352:
351:
347:
346:
345:
343:
342:
341:
322:
321:
302:
298:
149:
113:
110:
107:
104:
103:
81:
74:
12:
11:
5:
350:
348:
340:
339:
334:
324:
323:
297:
294:
288:
287:
286:
285:
284:
283:
282:
281:
252:
251:
250:
249:
248:
247:
233:
232:
231:
230:
216:
215:
214:
207:
206:
205:
196:
195:
148:
145:
142:
141:
138:
137:
134:
133:
126:
120:
119:
117:
100:the discussion
87:
86:
83:Science portal
70:
58:
57:
52:
40:
39:
33:
26:
13:
10:
9:
6:
4:
3:
2:
349:
338:
335:
333:
330:
329:
327:
320:
318:
314:
310:
306:
295:
293:
292:
280:
276:
272:
268:
264:
260:
259:
258:
257:
256:
255:
254:
253:
246:
243:
239:
238:
237:
236:
235:
234:
229:
225:
221:
217:
212:
211:
208:
203:
202:
200:
199:
198:
197:
194:
191:
186:
185:
184:
183:
179:
175:
169:
168:
167:
163:
159:
155:
131:
125:
122:
121:
118:
101:
97:
93:
92:
84:
78:
73:
71:
68:
64:
63:
59:
56:
53:
50:
46:
41:
37:
31:
27:
18:
17:
303:— Preceding
299:
290:
289:
271:Jitse Niesen
266:
220:Jitse Niesen
174:Jitse Niesen
170:
158:Jitse Niesen
152:Copied from
151:
150:
89:
36:WikiProjects
291:End of copy
326:Categories
309:82.0.88.79
242:Hermitian
190:Hermitian
305:unsigned
296:Example
105:Science
96:Science
55:Science
32:scale.
156:. --
313:talk
275:talk
224:talk
178:talk
162:talk
124:???
328::
315:)
277:)
226:)
180:)
164:)
311:(
273:(
222:(
176:(
160:(
132:.
38::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
