Nothing will be more central to computational science in the next century than the art of transforming a problem that appears intractable into another whose solution can be approximated rapidly.For Krylov subspace matrix iterations, this is preconditioning. -Trefethen Bau,1997. Lloyd N.Trefethen Professor of University of Oxford,Head of Oxford's Numerical Analysis Group First customer to buy MATLAB Royal Society(英国至家学会)，National Academy of Engineering(关国国家工程院)， Academia Europaea(欧洲人文与自然科乎院) Fellow of SIAM and AMS.President of SIAM IMA Gold Medal.LMS Naylor Prize.SIAM Polya Prize 包 SIAM John von Neumann Prize Invited speaker at ICIAM,ICM,and ECM congresses Author of SIAM's all-time bestseller Winner of teaching prizes at MIT.Cornell and Oxford Winner of the first Fox Prize in Numerical Analysis Inventor of Chebfun L.N.Trefethen and D.Bau,III,Numerical Linear Algebra,1997. http://aath.ecnu.edu.cn/-jypan 2/72Nothing will be more central to computational science in the next century than the art of transforming a problem that appears intractable into another whose solution can be approximated rapidly. For Krylov subspace matrix iterations, this is preconditioning. — Trefethen & Bau, 1997. Lloyd N. Trefethen Professor of University of Oxford, Head of Oxford’s Numerical Analysis Group  First customer to buy MATLAB  Royal Society (英国皇家学会), National Academy of Engineering (美国国家工程院), Academia Europaea (欧洲人文与自然科学院)  Fellow of SIAM and AMS, President of SIAM  IMA Gold Medal, LMS Naylor Prize, SIAM Pólya Prize  SIAM John von Neumann Prize  Invited speaker at ICIAM, ICM, and ECM congresses  Author of SIAM’s all-time bestseller  Winner of teaching prizes at MIT, Cornell and Oxford  Winner of the first Fox Prize in Numerical Analysis  Inventor of Chebfun  L.N. Trefethen and D. Bau, III, Numerical Linear Algebra, 1997. http://math.ecnu.edu.cn/~jypan 2/72