±±¾©Ê¯ÓÍ»¯¹¤Ñ§Ôº2026ÄêÑо¿ÉúÕÐÉú½ÓÊÕµ÷¼Á¹«¸æ
²é¿´: 3493  |  »Ø¸´: 10

mathstudy

½ð³æ (ÕýʽдÊÖ)


[½»Á÷] matlab Çó½âÏßÐÔ·½³Ì×éAx=b

x=inv(A)*b;ºÍx=A\b;ºÍµü´ú·¨  ÓÐÊ²Ã´Çø±ð£¿ Ç°ÃæÁ½¸öÇó AÄæ µÄÊÇ»ùÓÚʲô£¿
»Ø¸´´ËÂ¥

» ²ÂÄãϲ»¶

» ±¾Ö÷ÌâÏà¹Ø¼ÛÖµÌùÍÆ¼ö£¬¶ÔÄúͬÑùÓаïÖú:

» ÇÀ½ð±ÒÀ²£¡»ØÌû¾Í¿ÉÒԵõ½:

²é¿´È«²¿É¢½ðÌù

ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
»ØÌûÖ§³Ö ( ÏÔʾ֧³Ö¶È×î¸ßµÄǰ 50 Ãû )

tiancanrong

½ð³æ (СÓÐÃûÆø)


¡ï
Сľ³æ: ½ð±Ò+0.5, ¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
Èç¹ûÄãÒªÖªµÀinv(A)*bÓëGauss ÏûÔª·¨µÄÇø±ð£¬¾ÍÒªÖªµÀ¼ÆËã»úÔËËãºÍÄã×Ô¼ºÓñÊËãÊÇÓÐÇø±ðµÄ¡£ÄãÓñÊËã¿ÉÒÔÓ÷ÖÊý£¬ÀíÂÛÉÏÊÇûÓÐÎó²îµÄ£»È»¶ø¼ÆËã»úÔËËãʱÊÜÏÞÓÚÊýµÄ¾«¶È£¬ÀíÂÛÉÏÊÇÓÐÎó²îµÄ¡£ËùÒÔͬÑùµÄÌâÄ¿£¬¼ÆËã»úÓò»Í¬µÄËã·¨¾ÍÊÇÎó²î»òЧÂÊ»áÓвî±ð¡£ÁíÍâ˵һ¾ä£¬inv£¨A£©Ò²ÐèÒªºÜ¸´ÔӵļÆËãµÄ£¬GaussÏûÈ¥·¨Ò²ÐèÒªÌõ¼þµÄ¡£µ±È»ÁË£¬ÓÉÓÚÏÖÔÚµçÄÔµÄÈíÓ²¼þ¶¼ºÜÏȽøÁË£¬Ò»°ãµÄ·½³ÌËæ±ãʲô·½·¨½â¶¼Ã»Çø±ðÁË¡£
5Â¥2014-02-08 22:00:36
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

tiancanrong

½ð³æ (СÓÐÃûÆø)


¡ï
Сľ³æ: ½ð±Ò+0.5, ¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
ÎÒ´óÖ¿´ÁËÒ»ÏÂmatlab help£¬A\b ¸ù¾ÝAµÄÇé¿öÓõ½¼¸ÖÖ²»Í¬µÄËã·¨£¬Èç¹ûAÊÇÒ»¸ö·½Õó£¬bÊÇÒ»¸öÁÐÏòÁ¿£¬´ËʱAx=b¾ÍÊÇÄã˵µÄÏßÐÔ·½³Ì×飬\ÓõÄËã·¨¾ÍÊÇGaussÏûÈ¥·¨£»Èç¹ûA²»ÊÇ·½Õó£¬ÄÇôAx=b¾ÍÊÇÒ»¸ö¾ØÕ󷽳̣¬ÆäʵÕâʱºò¾«È·½â²»Ò»¶¨´æÔÚ£¬matlabÖеÄ\¾ÍÓÃÁË×îС¶þ³Ë·¨µÄ˼ÏëÇóÁËÒ»¸ö½üËÆµÄx£¨Ò²¿É³ÆÎª¹ãÒå½â£©£¬Ëã·¨ÊÇQR·Ö½â¡£

¿ÉÒÔÕâ¸ö¼òµ¥Àí½â£¬inv(A)*bÊÇA\bµÄÒ»ÖÖÌØÊâÇé¿ö£¨ÏßÐÔ·½³Ì×éʱ£©£¬µ«ÊÇA\b¸üÇ¿´ó£¬¿ÉÒÔÇó³ö¹ãÒå½â¡£
ÔÚ¼ÆËãÏßÐÔ·½³Ì×éAx=bʱ£¬inv(A)*bºÍA\bÓõÄÊýÖµËã·¨¶¼ÊÇGaussÏûÈ¥·¨¡£ÖÁÓÚÄã˵µÄЧÂÊ£¬A\bÓÉÓÚ¿¼ÂǵÄÇé¿ö±È½ÏÅӴ󣬵÷ÓõÄʱºòÉÔ΢»áÂýÒ»µã£¬ÎÒ²»ÈÏΪÓÐÖʵÄÇø±ð¡£
7Â¥2014-02-09 12:15:12
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
ÆÕͨ»ØÌû
¡ï
Сľ³æ: ½ð±Ò+0.5, ¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
A=[¡­¡­],  b=[¡­¡­],  s=rref([A,b])Ϊ¼Ñ£¬Èç¹û·ÇÂúÖÈ£¬Ò²¿ÉÖªµÀ¡£
2Â¥2014-02-07 13:28:11
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

´÷¸Ö¿øµÄÖíÍ·

ľ³æ (ÖªÃû×÷¼Ò)


¡ï
Сľ³æ: ½ð±Ò+0.5, ¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
Èç¹ûA²»ÊÇ·½Õó£¬ËüµÄÄæÊDz»´æÔڵġ£Õâʱinv(A)ÎÞ·¨Ó㬵«¿ÉÒÔÓùãÒåÄæpinv(A)¡£¶øA\bºÎʱ¶¼¿ÉÓá£

[ ·¢×ÔÊÖ»ú°æ http://muchong.com/3g ]
3Â¥2014-02-07 17:09:13
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

mathstudy

½ð³æ (ÕýʽдÊÖ)


AÊÇ¿ÉÄæ·½Õó£¬ ÎÒÏëÇë½ÌµÄµÄÊÇ  A\b ºÍ inv(A)*b ÖÐ ËûÃÇÇóAÄæµÄ Ô­Àí ÓÐÊ²Ã´Çø±ð£¬ Ϊʲô  A\b±È inv£¨A£©*b µÄЧÂʸߣ¿ ÁíÍâ  Èç¹ûÊÇ Gauss ÏûÔª·¨ÄØ£¿
4Â¥2014-02-07 19:11:12
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

mathstudy

½ð³æ (ÕýʽдÊÖ)


ÒýÓûØÌû:
5Â¥: Originally posted by tiancanrong at 2014-02-08 22:00:36
Èç¹ûÄãÒªÖªµÀinv(A)*bÓëGauss ÏûÔª·¨µÄÇø±ð£¬¾ÍÒªÖªµÀ¼ÆËã»úÔËËãºÍÄã×Ô¼ºÓñÊËãÊÇÓÐÇø±ðµÄ¡£ÄãÓñÊËã¿ÉÒÔÓ÷ÖÊý£¬ÀíÂÛÉÏÊÇûÓÐÎó²îµÄ£»È»¶ø¼ÆËã»úÔËËãʱÊÜÏÞÓÚÊýµÄ¾«¶È£¬ÀíÂÛÉÏÊÇÓÐÎó²îµÄ¡£ËùÒÔͬÑùµÄÌâÄ¿£¬¼ÆËã»úÓà ...

ÄÇ  inv(A)*bÓë Gauss ºÍA\b ÈýÕß  ÔÚmatlab ÉÏÃæµÄЧÂÊΪʲô²»Ò»Ñù£¿  ËûÃÇÔÚ matlab ÉϵÄÔËÐз½Ê½ÓÐÊ²Ã´Çø±ð£¿ (±ÈÈç˵ A\b ¿ÉÄÜÊÇ»ùÓÚLU ·Ö½â¶øÇó½â·½³ÌµÄ)
6Â¥2014-02-09 08:47:05
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

mathstudy

½ð³æ (ÕýʽдÊÖ)


ÒýÓûØÌû:
7Â¥: Originally posted by tiancanrong at 2014-02-09 12:15:12
ÎÒ´óÖ¿´ÁËÒ»ÏÂmatlab help£¬A\b ¸ù¾ÝAµÄÇé¿öÓõ½¼¸ÖÖ²»Í¬µÄËã·¨£¬Èç¹ûAÊÇÒ»¸ö·½Õó£¬bÊÇÒ»¸öÁÐÏòÁ¿£¬´ËʱAx=b¾ÍÊÇÄã˵µÄÏßÐÔ·½³Ì×飬\ÓõÄËã·¨¾ÍÊÇGaussÏûÈ¥·¨£»Èç¹ûA²»ÊÇ·½Õó£¬ÄÇôAx=b¾ÍÊÇÒ»¸ö¾ØÕ󷽳̣¬ÆäʵÕâʱ ...

лл°¡.....µ«ÊÇÎÒµÄÔËÐнá¹ûÏÔʾ  A\b±È×Ô¼ºµÄGauss³ÌÐò¿ìºÜ¶à
8Â¥2014-02-09 19:33:04
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

tiancanrong

½ð³æ (СÓÐÃûÆø)


¡ï
Сľ³æ: ½ð±Ò+0.5, ¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
ÒýÓûØÌû:
8Â¥: Originally posted by mathstudy at 2014-02-09 19:33:04
лл°¡.....µ«ÊÇÎÒµÄÔËÐнá¹ûÏÔʾ  A\b±È×Ô¼ºµÄGauss³ÌÐò¿ìºÜ¶à...

Äã×Ô¼º±àµÄGauss³ÌÐò£¬ºÍmatlab×Ô´øµÄ³ÌÐò¿âÀïµÄGaussËã·¨µ÷Óõķ½Ê½Ó¦¸ÃÓÐÇø±ðµÄ£¬Ç×¶ù×Óµ±È»¿ìÒ»µã¡£ÁíÍâÎÊһϣ¬ÄãÈçºÎ²âÊÔ³ÌÐòµÄ¿ìÂýµÄ£¿ÎªÊ²Ã´Òª²âÊÔ¿ìÂý£¿

[ Last edited by tiancanrong on 2014-2-10 at 12:26 ]
9Â¥2014-02-10 12:14:12
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

mathstudy

½ð³æ (ÕýʽдÊÖ)


ÒýÓûØÌû:
9Â¥: Originally posted by tiancanrong at 2014-02-10 12:14:12
Äã×Ô¼º±àµÄGauss³ÌÐò£¬ºÍmatlab×Ô´øµÄ³ÌÐò¿âÀïµÄGaussËã·¨µ÷Óõķ½Ê½Ó¦¸ÃÓÐÇø±ðµÄ£¬Ç×¶ù×Óµ±È»¿ìÒ»µã¡£ÁíÍâÎÊһϣ¬ÄãÈçºÎ²âÊÔ³ÌÐòµÄ¿ìÂýµÄ£¿ÎªÊ²Ã´Òª²âÊÔ¿ìÂý£¿
...

ºÃ°É  Ð»¹ýÁË    ²âÊÔʱ¼äµÄ»° ¿ÉÒÔÓÃcpuʱ¼ä°¡.  ÓеÄʱºò»¹ÊÇ×¢ÖØËã·¨µÄ¿ìÂýµÄ...
10Â¥2014-02-12 13:43:48
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

cced_1998

ľ³æ (СÓÐÃûÆø)


¡ï
Сľ³æ: ½ð±Ò+0.5, ¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
It takes almost two and one half times as long to compute the solution with y = inv(A)*b as with z = A\b. Both produce computed solutions with about the same error, 1.e-6, reflecting the condition number of the matrix. But the size of the residuals, obtained by plugging the computed solution back into the original equations, differs by several orders of magnitude. The direct solution produces residuals on the order of the machine accuracy, even though the system is badly conditioned.

The behavior of this example is typical. Using A\b instead of inv(A)*b is two to three times as fast and produces residuals on the order of machine accuracy, relative to the magnitude of the data.
11Â¥2016-03-31 21:37:38
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
Ïà¹Ø°æ¿éÌø×ª ÎÒÒª¶©ÔÄÂ¥Ö÷ mathstudy µÄÖ÷Ìâ¸üÐÂ
×î¾ßÈËÆøÈÈÌûÍÆ¼ö [²é¿´È«²¿] ×÷Õß »Ø/¿´ ×îºó·¢±í
[¿¼ÑÐ] 285Çóµ÷¼Á +4 ¶ñ·¨´ó¶þµÄÆøÎ¶ß 2026-04-05 5/250 2026-04-05 20:32 by 286640313
[¿¼ÑÐ] ¿¼ÑÐÉúÎïÓëÒ½Ò©µ÷¼Á +8 Ìúº©º©123425 2026-03-31 8/400 2026-04-05 20:28 by lys0704
[¿¼ÑÐ] 288Çóµ÷¼Á Ò»Ö¾Ô¸¹þ¹¤´ó ²ÄÁÏÓ뻯¹¤ +13 ÂåÉñ¸ç¸ç 2026-04-03 13/650 2026-04-05 17:27 by zzx2138
[¿¼ÑÐ] ²ÄÁÏר˶ µ÷¼Á +14 CXN123456 2026-04-03 14/700 2026-04-05 17:18 by Hdyxbekcb
[¿¼ÑÐ] 358Çóµ÷¼Á +7 Çïgk 2026-04-04 7/350 2026-04-05 13:29 by huangmoli
[¿¼ÑÐ] 271·ÖÇóµ÷¼ÁѧУ +12 zph158488£¡ 2026-04-02 13/650 2026-04-05 10:13 by lqwchd
[¿¼ÑÐ] ²ÄÁϵ÷¼Á +9 ¸ï΢¹ð 2026-04-04 9/450 2026-04-05 08:27 by 544594351
[¿¼ÑÐ] 283Çóµ÷¼Á +10 A child 2026-04-04 10/500 2026-04-05 08:22 by qlm5820
[¿¼ÑÐ] Ò»Ö¾Ô¸Ö£´ó0705Çóµ÷¼Á +3 éÙʮһ 2026-04-02 4/200 2026-04-05 00:05 by chongya
[¿¼ÑÐ] ¿É¿çרҵµ÷¼Á +3 ÖÜµÄµÃµØ 2026-04-04 6/300 2026-04-04 22:21 by barlinike
[¿¼ÑÐ] 309·Ö085801Çóµ÷¼Á +11 MY_angel 2026-03-31 11/550 2026-04-04 19:11 by À¶ÔÆË¼Óê
[¿¼ÑÐ] 265Çóµ÷¼Á +17 ÁÖÉîÎÂÀ½ 2026-04-01 20/1000 2026-04-04 01:09 by userper
[»ù½ðÉêÇë] esi¸ß±»ÒýÂÛÎÄÊDz»ÊÇÄܶÔÖбêÓÐËù¼Ó·ÖºÍ°ïÖúÄØ +5 redcom 2026-04-01 6/300 2026-04-03 15:15 by Howard28
[¿¼ÑÐ] Ò»Ö¾Ô¸±±¾©½»Í¨´óѧ²ÄÁϹ¤³Ì×Ü·Ö358 +4 cs0106 2026-04-03 4/200 2026-04-03 13:41 by °ÙÁéͯ888
[¿¼ÑÐ] 085801 ×Ü·Ö275 ±¾¿ÆÐÂÄÜÔ´ Çóµ÷¼Á +19 bradoner 2026-04-01 23/1150 2026-04-03 10:07 by linyelide
[¿¼ÑÐ] 326Çóµ÷¼Á +10 áÌáÌ×Ð 2026-04-02 10/500 2026-04-03 09:08 by ÅÁ¶ûÂíÀ­ÌØ
[¿¼ÑÐ] 302Çóµ÷¼Á +9 zyxÉϰ¶£¡ 2026-04-02 9/450 2026-04-02 23:07 by Âí¶ù¿ì¿ìµØÅÜ
[¿¼ÑÐ] 085601Ò»Ö¾Ô¸ÖÐɽ´óѧÉîÛÚ²ÄÁϹ¤³Ì330Çóµ÷¼Á +8 pipiver 2026-03-30 8/400 2026-04-02 12:01 by ms629
[¿¼ÑÐ] 324Çóµ÷¼Á +5 ÏëÉÏѧÇóµ÷ 2026-04-01 6/300 2026-04-02 10:16 by sanrepian
[¿¼ÑÐ] 348»·¾³¹¤³Ìµ÷¼Á +3 ÎâÑå׿24k 2026-04-01 3/150 2026-04-02 09:14 by nanaliuyun
ÐÅÏ¢Ìáʾ
ÇëÌî´¦ÀíÒâ¼û