2/ ERATO

Size: px
Start display at page:

Download "2/ 36 2012 2012 ERATO"

Transcription

1 , JST, ERATO,

2 2/ ERATO

3 Given n n A 1,..., A N Find P s.t. P A 1 P,..., P A N P A 1 A 2 A N simultaneously P A 1 P P A 2 P P A N P 3/ 36

4 4/ 36

5 5/ 36

6 6/ 36 [Wigner 1931 ]. [de Klerk-Dobre 2011] etc [Arima-Kim-Kojima 2012] etc [Burgdorf-Klep-Povh 2011] [Aiura-Kakimura-Murota 2011] [Gutch-Krumsiek-Theis 2011] [Irving-Sorrentino 2012].

7 7/ 36 [Wigner 1931 ] Hx = ϵx H = α 1 H α N H N H 1,..., H N

8 8/ 36 [Irving-Sorrentino 2012] x(t) = A 1 x(t 1) + + A N x(t N) x(t) t A k k A 1 A 2.

9 [Gatermann-Parrilo 2004], [Murota-Kanno-Kojima-Kojima 2010],... minimize C, X subject to A i, X = b i (i = 1,..., N) X O 7 days 7 mins [de Klerk-Dobre-Pasechnik 2009] 9/ 36

10 [Jutten-Herault 1985], [Cardoso-Soulomiac 1993],... Y 1 Y 2 Y l Given: Find: n X Y 1,..., Y l W P C P = X = W Y 10/ 36

11 11/ 36 [Wigner 1931 ]. [de Klerk-Dobre 2011] etc [Arima-Kim-Kojima 2012] etc [Burgdorf-Klep-Povh 2011] [Aiura-Kakimura-Murota 2011] [Gutch-Krumsiek-Theis 2011] [Irving-Sorrentino 2012].

12 12/ 36

13 13/ 36 SBD = SBD =

14 old new numerical linear algebra Jacobi-like [Bunse-Gerstner, Byers, Mehrmann 1990] JADE [Cardoso-Souloumiacc 1993] [Theis 2007] abstract algebra one-by-one [folklore -1820] The recipe [Schur 1905] MKKKM [Murota-Kanno-Kojima-Kojima MM [Maehara-Murota 2012] 14/ ]

15 old new numerical linear algebra Jacobi-like [Bunse-Gerstner, Byers, Mehrmann 1990] JADE [Cardoso-Souloumiacc 1993] [Theis 2007] abstract algebra one-by-one [folklore -1820] The recipe [Schur 1905] MKKKM [Murota-Kanno-Kojima-Kojima MM [Maehara-Murota 2012] 15/ ]

16 16/ 36 one-by-one method [ ]. A, X. wlog. X = diag(x 1,..., x n ), AX XA = [(x j x i )a ij ] = O x x y X A X A

17 17/ 36 Jacobi-like method [ ] (Bunse-Gerstner, Byers, Mehrmann 1990) one-by-one minimize [ off(p AP ) + off(p BP ) ] Givens 2 2 Jacobi

18 18/ 36 JADE [ ] (Cardoso, Souloumiac 1993) minimize [ off(p A 1 P ) + + off(p A N P ) ] Jacobi-like method 1 = by Cardoso

19 JADE [ ( )] (Theis 2007) minimize [ off(p A 1 P ) + + off(p A N P ) ] = [Maehara Gutch 2010] 19/ 36

20 old new numerical linear algebra Jacobi-like [Bunse-Gerstner, Byers, Mehrmann 1990] JADE [Cardoso-Souloumiacc 1993] [Theis 2007] abstract algebra one-by-one [folklore -1820] Schur lemma [Schur 1905] MKKKM [Murota-Kanno-Kojima-Kojima MM [Maehara-Murota 2012] 20/ ]

21 A 1,..., A N G Q A j Q = A j (Q G) G Schur - G A j - A j G G Schur lemma: MKKKM, MM: one-by-one 21/ 36

22 22/ 36 Schur lemma (Schur 1905) Q A j Q = A j (Q G) 1. A 1,..., A N G 2. G 3. A 1,..., A N 1930 Wigner cf. Heisenberg 1925

23 [Murota-Kanno-Kojima-Kojima 2010] 23/ 36 Q. 3V 3V (3i + j, 3k + l) k l i j A.

24 24/ 36 MKKKM [Murota-Kanno-Kojima-Kojima 2010, Maehara-Murota 2011] 1. A 1,..., A N cf: one-by-one

25 25/ 36 MKKKM [Murota-Kanno-Kojima-Kojima 2010, Maehara-Murota 2011] cf: one-by-one

26 26/ 36 MKKKM A 1,..., A N Artin-Wedderburn T := A 1,..., A N (M n1 I µ1 ) (M nl I µl ) T M n I µ one-by-one

27 MM [Maehara-Murota 2012] one-by-one X = diag(x 1,..., x n ), AX XA = [(x j x i )a ij ] = O x x X y A 1,..., A N X A 1,..., A N A 27/ 36

28 T := {X A i X X i A = O (i = 1,..., N)} 28/ 36 MM [Maehara-Murota 2012] 1. A i X XA i = O (i = 1,..., N) 2. X Artin-Wedderburn

29 29/ 36 MM [Maehara-Murota 2012] 1. A i X XA i ϵ (i = 1,..., N) 2. X ϵ ϵ

30 / maehara/commdec/ 30/ 36

31 31/ 36 A 1 A 2 A N simultaneously P A 1 P P A 2 P P A N P state of the art: [MM 2012]

32 32/ 36

33 33/ 36 preconditioning

34 A i X XA i = O (i = 1,..., N) X λ i λ j [Dyson index] n n exp( n λ 2 i /4) i<j λ i λ j i.e., λ i λ j cf. λ i λ j 2 34/ 36

35 35/ 36 T T = T 1 T l X T with n 2 k Dyson index ToDo:

36 A 1 A 2 A N simultaneously P A 1 P P A 2 P P A N P state of the art: [MM 2012] ( ) 36/ 36

a a b a b c d e R c d e A a b e a b a b c d a b c d e f a M a b f d a M b a b a M b a M b M M M R M a M b M c a M a R b A a b b a CF a b c a b a M b a b M a M b c a A b a b M b a A b a M b C a M C a M

More information

第85 回日本感染症学会総会学術集会後抄録(III)

第85 回日本感染症学会総会学術集会後抄録(III) β β α α α µ µ µ µ α α α α γ αβ α γ α α γ α γ µ µ β β β β β β β β β µ β α µ µ µ β β µ µ µ µ µ µ γ γ γ γ γ γ µ α β γ β β µ µ µ µ µ β β µ β β µ α β β µ µµ β µ µ µ µ µ µ λ µ µ β µ µ µ µ µ µ µ µ

More information

P-12 P-13 3 4 28 16 00 17 30 P-14 P-15 P-16 4 14 29 17 00 18 30 P-17 P-18 P-19 P-20 P-21 P-22

P-12 P-13 3 4 28 16 00 17 30 P-14 P-15 P-16 4 14 29 17 00 18 30 P-17 P-18 P-19 P-20 P-21 P-22 1 14 28 16 00 17 30 P-1 P-2 P-3 P-4 P-5 2 24 29 17 00 18 30 P-6 P-7 P-8 P-9 P-10 P-11 P-12 P-13 3 4 28 16 00 17 30 P-14 P-15 P-16 4 14 29 17 00 18 30 P-17 P-18 P-19 P-20 P-21 P-22 5 24 28 16 00 17 30 P-23

More information

001 No.3/12 1 1 2 3 4 5 6 4 8 13 27 33 39 001 No.3/12 4 001 No.3/12 5 001 No.3/12 6 001 No.3/12 7 001 8 No.3/12 001 No.3/12 9 001 10 No.3/12 001 No.3/12 11 Index 1 2 3 14 18 21 001 No.3/12 14 001 No.3/12

More information

1 913 10301200 A B C D E F G H J K L M 1A1030 10 : 45 1A1045 11 : 00 1A1100 11 : 15 1A1115 11 : 30 1A1130 11 : 45 1A1145 12 : 00 1B1030 1B1045 1C1030

1 913 10301200 A B C D E F G H J K L M 1A1030 10 : 45 1A1045 11 : 00 1A1100 11 : 15 1A1115 11 : 30 1A1130 11 : 45 1A1145 12 : 00 1B1030 1B1045 1C1030 1 913 9001030 A B C D E F G H J K L M 9:00 1A0900 9:15 1A0915 9:30 1A0930 9:45 1A0945 10 : 00 1A1000 10 : 15 1B0900 1B0915 1B0930 1B0945 1B1000 1C0900 1C0915 1D0915 1C0930 1C0945 1C1000 1D0930 1D0945 1D1000

More information

人芯経営論 ・・・リーダーシップ考②

人芯経営論 ・・・リーダーシップ考② 2009/12/15 2009/11/17 2009/11/16 2009/10/19 2009/10/15 2009/10/1 2009/9/17 2009/9/1 2009/8/17 2009/8/17 2009/8/14 2009/8/12 2009/7/28 2009/7/17 2009/7/15 2009/6/24 2009/6/18 2009/6/15 2009/5/20 2009/5/15

More information

O157 6/23 7/4 6 25 1000 117,050 6 14:00~15:30 1 2 22 22 14:30~15:30 8 12 1 5 20 6 20 10 11 30 9 10 6 1 30 6 6 0 30 6 19 0 3 27 6 20 0 50 1 2 6 4 61 1 6 5 1 2 1 2 6 19 6 4 15 6 1 6 30 6 24 30 59

More information

136 pp p µl µl µl

136 pp p µl µl µl 135 2006 PCB C 12 H 10-n Cl n n 1 10 CAS No. 42 PCB: 53469-21-9, 54 PCB: 11097-69-1 0.01 mg/m 3 PCB PCB 25 µg/l 136 pp p µl µl µl 137 1 γ 138 1 γ γ γ µl µl µl µl µl µl µl l µl µl µl µl µl l 139 µl µl µl

More information

第18回海岸シンポジウム報告書

第18回海岸シンポジウム報告書 2011.6.25 2011.6.26 L1 2011.6.27 L2 2011.7.6 2011.12.7 2011.10-12 2011.9-10 2012.3.9 23 2012.4, 2013.8.30 2012.6.13 2013.9 2011.7-2011.12-2012.4 2011.12.27 2013.9 1m30 1 2 3 4 5 6 m 5.0m 2.0m -5.0m 1.0m

More information

液晶ディスプレイ取説TD-E432/TD-E502/TD-E552/TD-E652/TD-E432D/TD-E502D

液晶ディスプレイ取説TD-E432/TD-E502/TD-E552/TD-E652/TD-E432D/TD-E502D 1 2 3 4 5 6 7 1 2 3 4 5 6 7 2 2 2 1 1 2 9 10 11 12 13 14 15 16 17 1 8 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 9 11 12 13 13 14 15 16 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 2 3 4 5 6 7 8 9 11 12

More information

000-.\..

000-.\.. 1 1 1 2 3 4 5 6 7 8 9 e e 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 10mm 150mm 60mm 25mm 40mm 30mm 25 26 27 1 28 29 30 31 32 e e e e e e 33 e 34 35 35 e e e e 36 37 38 38 e e 39 e 1 40 e 41 e 42 43

More information

1 1 36 223 42 14 92 4 3 2 1 4 3 4 3429 13536 5 6 7 8 9 2.4m/ (M) (M) (M) (M) (M) 6.67.3 6.57.2 6.97.6 7.27.8 8.4 5 6 5 6 5 5 74 1,239 0 30 21 ( ) 1,639 3,898 0 1,084 887 2 5 0 2 2 4 22 1 3 1 ( :) 426 1500

More information

1 C 2 C 3 C 4 C 1 C 2 C 3 C

1 C 2 C 3 C 4 C 1 C 2 C 3 C 1 e N >. C 40 41 2 >. C 3 >.. C 26 >.. C .mm 4 C 106 e A 107 1 C 2 C 3 C 4 C 1 C 2 C 3 C 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124

More information

1 2 http://www.japan-shop.jp/ 3 4 http://www.japan-shop.jp/ 5 6 http://www.japan-shop.jp/ 7 2,930mm 2,700 mm 2,950mm 2,930mm 2,950mm 2,700mm 2,930mm 2,950mm 2,700mm 8 http://www.japan-shop.jp/ 9 10 http://www.japan-shop.jp/

More information

1 911 34/ 22 1012 2/ 20 69 3/ 22 69 1/ 22 69 3/ 22 69 1/ 22 68 3/ 22 68 1/ 3 8 D 0.0900.129mm 0.1300.179mm 0.1800.199mm 0.1000.139mm 0.1400.409mm 0.4101.199mm 0.0900.139mm 0.1400.269mm 0.2700.289mm

More information

DiMAGE Scan Multi PRO

DiMAGE Scan Multi PRO J 9229-2887-26 P-A111 9229-2887-24 X-A110 9229-2887-24

More information

0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c), (6) ( b) c = (b c), (7) (b + c) = b + c, (8) ( + b)c = c + bc (9

0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c), (6) ( b) c = (b c), (7) (b + c) = b + c, (8) ( + b)c = c + bc (9 1-1. 1, 2, 3, 4, 5, 6, 7,, 100,, 1000, n, m m m n n 0 n, m m n 1-2. 0 m n m n 0 2 = 1.41421356 π = 3.141516 1-3. 1 0 1-4. 1-5. (1) + b = b +, (2) b = b, (3) + 0 =, (4) 1 =, (5) ( + b) + c = + (b + c),

More information

106 4 4.1 1 25.1 25.4 20.4 17.9 21.2 23.1 26.2 1 24 12 14 18 36 42 24 10 5 15 120 30 15 20 10 25 35 20 18 30 12 4.1 7 min. z = 602.5x 1 + 305.0x 2 + 2

106 4 4.1 1 25.1 25.4 20.4 17.9 21.2 23.1 26.2 1 24 12 14 18 36 42 24 10 5 15 120 30 15 20 10 25 35 20 18 30 12 4.1 7 min. z = 602.5x 1 + 305.0x 2 + 2 105 4 0 1? 1 LP 0 1 4.1 4.1.1 (intger programming problem) 1 0.5 x 1 = 447.7 448 / / 2 1.1.2 1. 2. 1000 3. 40 4. 20 106 4 4.1 1 25.1 25.4 20.4 17.9 21.2 23.1 26.2 1 24 12 14 18 36 42 24 10 5 15 120 30

More information

地域総合研究第40巻第1号

地域総合研究第40巻第1号 * abstract This paper attempts to show a method to estimate joint distribution for income and age with copula function. Further, we estimate the joint distribution from National Survey of Family Income

More information

1: *2 W, L 2 1 (WWL) 4 5 (WWL) W (WWL) L W (WWL) L L 1 2, 1 4, , 1 4 (cf. [4]) 2: 2 3 * , , = , 1

1: *2 W, L 2 1 (WWL) 4 5 (WWL) W (WWL) L W (WWL) L L 1 2, 1 4, , 1 4 (cf. [4]) 2: 2 3 * , , = , 1 I, A 25 8 24 1 1.1 ( 3 ) 3 9 10 3 9 : (1,2,6), (1,3,5), (1,4,4), (2,2,5), (2,3,4), (3,3,3) 10 : (1,3,6), (1,4,5), (2,2,6), (2,3,5), (2,4,4), (3,3,4) 6 3 9 10 3 9 : 6 3 + 3 2 + 1 = 25 25 10 : 6 3 + 3 3

More information

2004 Copyright by Tatsuo Minohara Programming with Mac OS X in Lambda 21 - page 2

2004 Copyright by Tatsuo Minohara Programming with Mac OS X in Lambda 21 - page 2 Living with Mac OS X in Lambda 21 2004 Copyright by Tatsuo Minohara Programming with Mac OS X in Lambda 21 - page 1 2004 Copyright by Tatsuo Minohara Programming with Mac OS X in Lambda 21 - page 2 2004

More information

MacOSXLambdaJava.aw

MacOSXLambdaJava.aw Living with Mac OS X in Lambda 21 2005 Copyright by Tatsuo Minohara Programming with Mac OS X in Lambda 21 - page 1 2005 Copyright by Tatsuo Minohara Programming with Mac OS X in Lambda 21 - page 2 2005

More information

n-5-1

n-5-1 5 8 所 得 区 分 3 回 までの 限 度 額 4 回 目 以 降 2 A 上 位 所 得 世 帯 1 B 一 般 世 帯 C 市 民 税 非 課 税 世 帯 150.000 円 + ( 医 療 費 500.000 円 ) 1% 83.400 円 80.100 円 + ( 医 療 費 267.000 円 ) 1% 44.400 円 35.400 円 24.600 円 保 険 外 ハ シ

More information

AHPを用いた大相撲の新しい番付編成

AHPを用いた大相撲の新しい番付編成 5304050 2008/2/15 1 2008/2/15 2 42 2008/2/15 3 2008/2/15 4 195 2008/2/15 5 2008/2/15 6 i j ij >1 ij ij1/>1 i j i 1 ji 1/ j ij 2008/2/15 7 1 =2.01/=0.5 =1.51/=0.67 2008/2/15 8 1 2008/2/15 9 () u ) i i i

More information

98 3 19 1853 80 14 2,450 19 4 5 6 7 1860 8 9 10 11 19 1 28 27 36 1962 2..1959 19951840 1914 2001 36 1869 18941998 1994 3 11 1314 12001 4 1201941 5 120

98 3 19 1853 80 14 2,450 19 4 5 6 7 1860 8 9 10 11 19 1 28 27 36 1962 2..1959 19951840 1914 2001 36 1869 18941998 1994 3 11 1314 12001 4 1201941 5 120 97 312013 97 118,. 31 2013. 97 118 港 湾 都 市 長 崎 における 近 代 交 通 体 系 の 形 成 過 程 1 ABSTRACT...,.......,. 1 2 1 98 3 19 1853 80 14 2,450 19 4 5 6 7 1860 8 9 10 11 19 1 28 27 36 1962 2..1959 19951840 1914 2001

More information