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笆�繝励Ο繧ｰ繝ｩ繝��育�皮ｩｶ驛ｨ莨夐未菫るΚ蛻�ｼ�:
9:30-10:15 繝√Η繝ｼ繝医Μ繧｢繝ｫ Tutorial Lecture �井ｼ∫判 陦悟�繝ｻ蝗ｺ譛牙､蝠城｡後�隗｣豕輔→縺昴�蠢懃畑遐皮ｩｶ驛ｨ莨夲ｼ� 蜿ｸ莨� 騾滓ｰｴ 隰呻ｼ亥嵜遶区ュ蝣ｱ蟄ｦ遐皮ｩｶ謇��
The numerical approximation of matrix functions
Michael Eiermann (Technische Universitat Bergakademie Freiberg)
Abstract
10:30-12:15 陦悟�繝ｻ蝗ｺ譛牙､蝠城｡後�隗｣豕輔→縺昴�蠢懃畑 Matrix Computation (1) 蠎ｧ髟ｷ 蠑ｵ 邏ｹ濶ｯ�亥錐蜿､螻句､ｧ蟄ｦ��
蜉�騾溷梛 ILU(0) 蛻�ｧ｣蜑榊�逅�▽縺� CRS 豕輔�蜿取據諤ｧ隧穂ｾ｡
笳句ｰｾ荳� 蜍�ｻ具ｼ井ｹ晏ｷ槫､ｧ蟄ｦ蟾･蟄ｦ驛ｨ B4�会ｼ瑚陸驥� 貂�ｬ｡�井ｹ晏ｷ槫､ｧ蟄ｦ諠��ｱ蝓ｺ逶､繧ｻ繝ｳ繧ｿ繝ｼ�会ｼ碁仭驛ｨ 驍ｦ鄒趣ｼ亥ｲ宣�閨門ｾｳ蟄ｦ蝨貞､ｧ蟄ｦ��
BiCR豕輔ｒ繝吶�繧ｹ縺ｫ譁ｰ縺励￥謠先｡医＆繧後◆CRS豕輔↓縺�ｍ縺�ｍ縺ｪ蜑榊�逅�ｒ
邨�∩蜷医ｏ縺帙◆縺ｨ縺阪�蜿取據諤ｧ縲��大ｼｷ諤ｧ縺昴＠縺ｦ蜉ｹ邇�↓縺､縺�※蝣ｱ蜻翫☆繧九�
ib_IC_0(tol) 蛻�ｧ｣蜑榊�逅��髢ｾ蛟､萓晏ｭ俶ｧ縺ｫ縺､縺�※
笳貴oethuthu�井ｹ晏ｷ槫､ｧ蟄ｦ螟ｧ蟄ｦ髯｢ D1�会ｼ瑚陸驥� 貂�ｬ｡�井ｹ晏ｷ槫､ｧ蟄ｦ諠��ｱ蝓ｺ逶､繧ｻ繝ｳ繧ｿ繝ｼ�会ｼ悟｡ｩ蜃ｺ 莠ｮ�井ｹ晏ｷ槫､ｧ蟄ｦ螟ｧ蟄ｦ髯｢ M2��
Inverse-based縺ｫ蝓ｺ縺･縺上ラ繝ｭ繝�ヴ繝ｳ繧ｰ繧剃ｽｿ縺｣縺櫑C蛻�ｧ｣縺､縺垢G豕�
縺ｮ髢ｾ蛟､縺ｫ蟇ｾ縺吶ｋ蜿取據諤ｧ縺ｫ縺､縺�※蝣ｱ蜻翫☆繧九�
BiCRSafe 豕輔�謠先｡医→螳牙�蜿取據諤ｧ縺ｮ隧穂ｾ｡
笳玖陸驥� 貂�ｬ｡�井ｹ晏ｷ槫､ｧ蟄ｦ諠��ｱ蝓ｺ逶､繧ｻ繝ｳ繧ｿ繝ｼ�会ｼ悟ｰｾ荳� 蜍�ｻ具ｼ井ｹ晏ｷ槫､ｧ蟄ｦ蟾･蟄ｦ驛ｨ B4�会ｼ碁仭驛ｨ 驍ｦ鄒趣ｼ亥ｲ宣�閨門ｾｳ蟄ｦ蝨貞､ｧ蟄ｦ��
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螳滄圀縺ｮ陦悟�縺ｫ縺､縺�※蜿取據螳牙�諤ｧ繧定ｪｿ縺ｹ縺溘�縺ｧ邨先棡繧貞�ｱ蜻翫☆繧九�
Finger pattern 縺ｮ繝悶Ο繝�け蛹悶↓繧医ｋ髯ｰ逧� wavelet 霑台ｼｼ騾�｡悟�蜑榊�逅��鬮倬溷喧
笳倶ｻ雁� 證�ｼ亥錐蜿､螻句､ｧ蟄ｦ螟ｧ蟄ｦ髯｢蟾･蟄ｦ遐皮ｩｶ遘� M1�会ｼ梧嵜謌鷹Κ 遏･蠎�ｼ亥錐蜿､螻句､ｧ蟄ｦ螟ｧ蟄ｦ髯｢蟾･蟄ｦ遐皮ｩｶ遘托ｼ会ｼ悟ｼｵ 邏ｹ濶ｯ�亥錐蜿､螻句､ｧ蟄ｦ螟ｧ蟄ｦ髯｢蟾･蟄ｦ遐皮ｩｶ遘托ｼ�
騾｣遶具ｼ第ｬ｡譁ｹ遞句ｼ上↓蟇ｾ縺吶ｋKrylov驛ｨ蛻�ｩｺ髢捺ｳ輔�蜑榊�逅�→縺励※,
霑台ｼｼ騾�｡悟�蜑榊�逅�ｳ輔′縺ゅｋ. 霑大ｹｴ, 縺薙�蜑榊�逅�ｳ輔↓蟇ｾ縺励※wavelet螟画鋤
繧貞茜逕ｨ縺吶ｋ遐皮ｩｶ縺瑚｡後ｏ繧後※縺�ｋ. 譛ｬ遐皮ｩｶ縺ｧ縺ｯ, finger pattern繧偵ヶ繝ｭ繝�け蛹�
縺吶ｋ縺薙→縺ｧ, 縺薙�蜑榊�逅�｡悟�繧偵ｈ繧企ｫ倬溘↓豎ゅａ繧区婿豕輔ｒ謠先｡医☆繧�.
Preconditioned Krylov Subspace Methods for the Solution of Least-Squares Problems
笳徽un-Feng Yin�亥嵜遶区ュ蝣ｱ蟄ｦ遐皮ｩｶ謇�会ｼ碁滓ｰｴ 隰� �亥嵜遶区ュ蝣ｱ蟄ｦ遐皮ｩｶ謇��
We compare preconditioned GMRES, CGLS and LSQR methods
for the solution of large sparse least-squares problems
by numerical experiments. As preconditioners, we use
a class of incomplete QR factorization based on Givens
rotation and RIF (Robust Incomplete Factorization).
Cutoff 縺励◆陦悟�縺ｫ蟇ｾ縺励※逍手｡悟�逕ｨ逶ｴ謗･豕輔ｒ逕ｨ縺�◆蜑榊�逅�→蜿榊ｾｩ豕輔↓縺､縺�※
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2驥榊ｯｾ隗定｡悟�縺ｮ迚ｹ逡ｰ蛟､險育ｮ励�縺溘ａ縺ｮdqds豕輔↓縺翫＞縺ｦ�後す繝輔ヨ縺ｨ縺励※
譛蟆丞崋譛牙､縺ｫ蟇ｾ縺吶ｋOstrowski荳狗阜縺翫ｈ縺ｳBrauer荳狗阜繧堤畑縺�◆蝣ｴ蜷医�
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Jacobi-Davidson豕輔↓逹逶ｮ縺励∽ｿｮ豁｣譁ｹ遞句ｼ上�豎りｧ｣縺ｧ縺ｩ繧薙↑逶ｴ莠､蛹悶�邁｡逡･蛹悶′險ｱ縺輔ｌ繧九°縲�
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蝗ｺ譛牙､隗｣豕輔〒蠢�ｦ√→縺輔ｌ繧句�鬆伜沺謗ｨ螳壹↓蠢懃畑縺励◆萓九ｒ遉ｺ縺吶�
螟ｧ隕乗ｨ｡逍手｡悟�縺ｫ蟇ｾ縺吶ｋ Grid 迺ｰ蠅�髄縺� Arnoldi 豕�
笳区惠蜴� 蟠�匱�育ｭ第ｳ｢螟ｧ蟄ｦ螟ｧ蟄ｦ髯｢繧ｷ繧ｹ繝�Β諠��ｱ蟾･蟄ｦ遐皮ｩｶ遘� M1�会ｼ悟ｰ冗ｧ 鄒ｩ荵�ｼ育ｭ第ｳ｢螟ｧ蟄ｦ螟ｧ蟄ｦ髯｢繧ｷ繧ｹ繝�Β諠��ｱ蟾･蟄ｦ遐皮ｩｶ遘� M2�会ｼ悟､夂伐驥� 蟇帑ｺｺ�育ｧ大ｭｦ謚陦捺険闊域ｩ滓ｧ具ｼ会ｼ梧ｫｻ莠� 驩�ｹ滂ｼ育ｭ第ｳ｢螟ｧ蟄ｦ螟ｧ蟄ｦ髯｢繧ｷ繧ｹ繝�Β諠��ｱ蟾･蟄ｦ遐皮ｩｶ遘托ｼ�
霑大ｹｴ�檎ｧ大ｭｦ謚陦楢ｨ育ｮ励↓縺翫＞縺ｦ螟ｧ隕乗ｨ｡縺ｪ蝗ｺ譛牙､蝠城｡後′迴ｾ繧後ｋ縺薙→縺悟､壹￥��
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螟夐㍾繝ｪ繧ｹ繧ｿ繝ｼ繝井ｻ倥″Arnoldi豕輔′縺ゅｋ��
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隍�ｴ�繝｢繝ｼ繝｡繝ｳ繝医�險育ｮ励ｒ蝗樣∩縺暦ｼ碁ｫ倡ｲｾ蠎ｦ縺ｮ蝗ｺ譛牙､�悟所縺ｳ蝗ｺ譛峨�繧ｯ繝医Ν縺瑚ｨ育ｮ励〒縺阪ｋ
縺薙→繧堤､ｺ縺呻ｼ�
Inexact Newton iteration method for a class of nonsymmetric algebraic Riccati equations
笳戯ong-hua Gao��Chinese Academy of Sciences D3��
We construct a class of inexact Newton iteration methods for a class of
Riccati equations, which use Newton iteration method as outer iteration and
doubling method as inner iteration.
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