高等教育出版社：《数值分析》书籍教材PDF电子版（第七版，共十二章，NUMERICAL ANALYSIS，Richard L. Burden、J. Douglas Faires）.pdf_大学文库

前言 20世纪未，以计算机和通信技术为代表的信息科学和技术，对世界的经济、军事、科技、教育、文化、卫生等方面的发展产生了深刻的影响，由此而兴起的信息产业己经成为世界经济发展的支柱。进入21世纪，各国为了加快本国的信息产业，加大了资金投入和政策扶持。为了加快我国信息产业的进程，在我国《国民经济和社会发展第十个五年计划纲要》中，明确提出“以信息化带动工业化，发挥后发优势，实现社会生产力的跨越式发展。”信息产业的国际竟争将日趋藏烈。在我国加入WT0后，我国信息产业将面临国外竞争对手的严峻挑战。竞争成败最终将取决于信息科学和技术人才的多少与优劣。在20世纪末，我国信息产业虽然得到迅猛发展，但与国际先进国家相比，差距还很大。为了赶上并超过国际先进水平，我国必须加快信息技术人才的培养，特别要培养一大批具有国际竞争能力的高水平的信息技术人才，促进我国信息产业和国家信息化水平的全面提商。为此，教商部高等教育司根据教商部吕福源副部长的意见，在长期重视推动高等学校信息科学和技术教学的基础上，将实施超前发展战略，采取一些重要举措，加快推动高等学校的信息科学和技术等相关专业的教学工作。在大力宣传、推荐我国专家编著的面向21世纪和“九五”重点的信息科学和技术课程教材的基础上，在有条件的高等学校的某些信息科学和技术课程中推动使用国外优秀教材的影印版进行英语或双语教学，以缩短我国在计算机教学上与国际先进水平的差距，同时也有助于强化我国大学生的英语水平。为了达到上述目的，在分析一些出版社已影印相关教材，一些学校已试用影印教材进行教学的基础上，教育部高等教育司组织并委托高等教育出版社开展国外优秀信息科学和技术优秀教材及其教学辅助材料的引进研究与影印出散的试点工作。为推动用影印版教材进行教学创造条件。本次引进的系列教材的影印出版工作，是在对我国高校信息科学和技术专业的课程与美国高校的进行对比分析的基础上展开的；所影印出版的教材均由我国主要高校

Preface About the Text We have developed this material for a sequence of courses on the theory and application of numerical approximation techniques.The text is designed primarily for junior-level math- ematics,science,and engineering majors who have completed at least the first year of the standard college calculus sequence.Familiarity with the fundamentals of matrix algebra and differential equations is also useful,but adequate introductory matcrial on these topics is prese ented in the text so thal those cours ed not be prerequi isites Previo In some cases.the m techniques was emphasized rather than the methods themselves;in others,the emphasis was reversed.The book has also been used as the core reference for courses at the beginning graduate level in engineering and computer science programs,and in first-year courses in introductory analysis offered at international universities.We have tried to adapt the book to fit these diverse users without compromising our original purpose: ean introduction to modern upproximation techniques. y ca sis for future studyof numerical analysis and scientific computing. The book contains sufficient material for a full year of study,but we expect many readers to use the text only for a single-term course.In such a coursc.students learn to identify the types of problems that require numerical techniques for their solution and see examples of the error propagation that can occur when numerical methods are applied. They accurately approximate the solutions of problems that cannot be solved exactly and lear techniques for estimatingeo bounds for the approximations.The remaindcr of the ext serve ce for ethods that are not c onsidered in the coursc.Either the atme ns of the ed b and edition contains more than 2 es ranging fron ntary appl and algorithms to generalizations and extensions of the theory.n addition the exercis sets include many applied problems from diverse areas of engineering,as well as from the physical,computer,biological,and social sciences.The applications chosen demonstrate concisely how numerical methods can be,and often must be.applied in real-life situations. A number of software packages have been developed to produce symbolic mathemat- domamong them in the academic envirmt are Derive matica Student ve ersions of these software packages are available at

Preface reasonable prices for most common computer systems.Although there are significant dif- ferences among the packages,both in performance and price,all can perform standard algebra and calculus operations.Having a symbolic computation package available can be very useful in the study of approximation techniques.The results in most of our examples and exercises have been g rated using problems for which exact values can be dete mined since this nits the metbod to he Exact solution 06 ed qute easily ng symbolic tion.n chniques the error analysis requires bounding a higher ordinar partial derivative of a function,which can be a tedious task and one that is not particularly instructive once the techniques of calculus have been mastered.Derivatives can be quickly obtained symbolically,and a little insight often permits a symbolic computation to aid in the bounding process as well. We have chosen Maple as our standard package because of its wide distribution,but Derive or mathematica can be substituted with only minor modifications.Examples and ercises have been added whene ver we felt that a comp uter algebra systemn would be of ant benefit,and we have cussed the approxima ion methods that Maple employs when it is ur eto solve a problem exactly. New for This Edltion The seventh edition includes two new major sections.The Preconditioned Conjugate Gra- dien pter 7 to provide a more complete treatm ent of the nu to systems of line sIt is pre esented as an ite ative s.In this form appr ma ite linear system rly useful for approximating the solution to large sparse systems In Chapter 10 we have added a section on Homotopy and Continuation methods.The s methods provide a distinctly different technique for approximating the solutions to nonlin ear systems of equations,one that has attracted a great deal of attention recently. We have also added extensive listings of Maple code throughout the book,since re viewers found this feature useful in the sixth edition.We have updated all the Maple code to Release 6.the version that will be current by the time the book is printed.Those familiar ith ast editi will find that virtu ally e ery roved in some way ve be ew ex he hope you will find these changes beneficial to the teaching a ysis;most have been motivated by changes in the presentation of the material to our own students. Another important modification in this edition is a web site at http://www.as.ysu.edu/~faires/Numerical-Analysis/ On this web site we will place updated programs s as the softwa responses to comments made by users of the book.We can th might be included in subsequent editions in the form of PDF files that users can download Our hope is that this will extend the life of the seventh edition while keeping the material in the book up to date

Preface xi Algorithms As in previous editions,we give a detailed,structured algorithm without program listing for each method in the text.The algorithms are in a form that can be coded,even by those with limited programming experience. This edition cudes a disk containing progr the algor ams for solutions to r esentative exer- The Maple and Mathema in MATLAB枣 a,as well a a comnputer software package that is wi y used for linear algebra applica systems. A Student Study Guide is available with this edition that illustrates the calls required for these programs,which is useful for those with limited programming experience.The study guide also contains worked-out solutions to many of the problems. Brooks/Cole can provide instructors with an Instructor's Manual that provides an- book.Com tion sults in the nstructor' were reg ed for this editio using the programs on lisk to ensure com patibi ty am ong the va ous programming systems The algorithms in the text lead to programs that give correct results for the examples and exercises in the text,but no attempt was made to write general-purpose professional software.Specifically,the algorithms are not always written in a form that leads to the mosf efficient program in terms of either time or storage requirements.When a conflict occurred between writing an extremely efficient algorithm and writing a slightly different one that better illustrates the important features of the method.the latter path was invariably taken About the Program Disk The CD on the inside back cover of the book contains the book ograms for all the algorithms in 11 in both the S)and ble udy Gu uide fo r the book (PDE ats For each algoithm there is a C.Fortran,Maple,Ma B,and Pascal program,and for some of these systems there are multiple programs that depend on the particular version of the software that is being run.Every program is illustrated with a sample problem that is closely correlated to the text.This permits the program to be run initially in the language of your choice to see the form of the input and output.The pro- grams can then be modified for other problems by making minor changes.The form of the nput and output are,as nearly as possible,the same in e ach of the p n ins structor using th e ally. without regard to the particular progra studer t uses quired is a computer running MS-DOS,Windows,or the Macintosh operating system You will,however,need appropriate software,such as a compiler for Pascal,Fortran,and C.or one of the computer algebra systems (Maple,Mathematica,and MATLAB).There

Preface xili Acknowledgments aa communicate are taken very seriously;we have tried to include all the suggestions that are in line with the philosophy of the book,and are extremely grateful to all those that have taken the time to contact us and inform us of improvements we can make in subsequent versions. We would particularly like to thank the following.whose efforts we greatly appreciate. Glen Granzow,Idaho State University Jose Miguel,Universidad Peruana Cayetano Heredia,Lima,Peru John M.Neuberger,Northern Arizona University L.G.de Pillis,Harvey Mudd College We want especially to thank our friend and former student Jim Baglama of Ball State University.Jim agreed to be an extensive reviewer for this edition and was particularly helpful in updating our survey sections and references to software.It is most gratifying to see one's students move through the profession. Also moving through his profession.but in a completly different manner,is our Editor and Publisher Gar y has been ar outstanding ma ager of our projects and al friend.We will ss his directic assista this opporunity to wish all the best in his upcoming retirement from Brooks/Cole As has been our practice in past editions of the book,we have used student help at Youngstown State University in preparing the seventh edition.Our able assistant for this edition was Laurie Marinelli,whom we thank for all her work.We would also like to express gratitude to our colleagues on the faculty and administration of Youngstown State University for providing us the opportunity and facilities to compiete this project. Finally,we would like to thank all those who have used and adopted the various edi tions of Nu rical Analysis over the ears.it has been wonderful to hear from so many and facult wwe hope osure to the study of nu rical is.If you edino ftre eitions of the bo ents studying nume analy e ments.We can be contacted by electronic mail at the addresses listed below. Richard L.Burden burden@math.ysu.edu J.Douglas Faires faires@math.ysu.edu