Preface Mathematica, and MATLAB). The Java implementations are an exception. You need the system to run the but Java can be freely downloaded from various sites. The best way to obtain Java is to use a search engine to search on the name, choose a download site, and follow the instructions for that site New for this edition The first edition of this book was published more than 30 years ago, in the decade after major advances in numerical techniques were made to reflect the new widespread availability of omputer equipment. In our revisions of the book we have added new techniques in order to keep our treatment current. To continue this trend, we have made a number of significant Our treatment of Numerical Linear Algebra has been extensively expanded, and con stitutes one of major changes in this edition. In particular, a section on Singular Value Decomposition has been added at the end of Chapter 9. This required a complete rewrite of the early part of Chapter 9 and considerable expansion of Chapter 6 to include neces- lry material concerning symmetric and orthogonal matrices. Chapter 9 is approximately 40% longer than in the eighth edition, and contains a significant number of new examples and exercises. Although students would certainly benefit from a course in Linear Algebra before studying this material, sufficient background material is included in the book, and every result whose proof is not given is referenced to at least one commonly available All the Examples in the book have been rewritten to better emphasize the problem to be solved before the specific solution is presented. Additional steps have been added to many of the examples to explicitly show the computations required for the first steps of iteration processes. This gives the reader a way to test and debug programs the ey have written for problems similar to the examples a new item designated as an illustration has been added This is used when discussing a specific application of a method not suitable for the problem statement-solution format of the Examples The Maple code we include now follows, whenever possible, the material included in their NumericalAnalysis package. The statements given in the text are precisely what is needed for the Maple worksheet applications, and the output is given in the same font and color format that Maple produces Anumber of sections have been expanded, and some divided, to make it easier for instruc- tors to assign problems immediately after the material is presented. This is particularly true in Chapters 3, 6, 7, and 9. Numerous new historical notes have been added, primarily in the margins where they can be considered independent of the text material. Much of the current material used in Numerical Analysis was developed in middle of the 20th century, and students should b The bibliographic material has been updated to reflect new editions of books that we reference. New sources have been added that were not previously available. As always with our revisions, every sentence was examined to determine if it was phrased in a manner that best relates what is described Copyright 2010 Cengage Learning. All Rights t materially affect the overall leaming eaperience Cengage Learning reserves the right to remo rty commen may be suppressed from the eBook andor eChaptert'sh. May no be copied, scanned, or duplicated, in whole or in part Due toPreface xi Mathematica, and MATLAB). The Java implementations are an exception. You need the system to run the programs, but Java can be freely downloaded from various sites. The best way to obtain Java is to use a search engine to search on the name, choose a download site, and follow the instructions for that site. New for This Edition The first edition of this book was published more than 30 years ago, in the decade after major advances in numerical techniques were made to reflect the new widespread availability of computer equipment. In our revisions of the book we have added new techniques in order to keep our treatment current. To continue this trend, we have made a number of significant changes to the ninth edition. • Our treatment of Numerical Linear Algebra has been extensively expanded, and con￾stitutes one of major changes in this edition. In particular, a section on Singular Value Decomposition has been added at the end of Chapter 9. This required a complete rewrite of the early part of Chapter 9 and considerable expansion of Chapter 6 to include neces￾sary material concerning symmetric and orthogonal matrices. Chapter 9 is approximately 40% longer than in the eighth edition, and contains a significant number of new examples and exercises. Although students would certainly benefit from a course in Linear Algebra before studying this material, sufficient background material is included in the book, and every result whose proof is not given is referenced to at least one commonly available source. • All the Examples in the book have been rewritten to better emphasize the problem to be solved before the specific solution is presented. Additional steps have been added to many of the examples to explicitly show the computations required for the first steps of iteration processes. This gives the reader a way to test and debug programs they have written for problems similar to the examples. • A new item designated as an Illustration has been added. This is used when discussing a specific application of a method not suitable for the problem statement-solution format of the Examples. • The Maple code we include now follows, whenever possible, the material included in their NumericalAnalysis package. The statements given in the text are precisely what is needed for the Maple worksheet applications, and the output is given in the same font and color format that Maple produces. • A number of sections have been expanded, and some divided, to make it easier for instruc￾tors to assign problems immediately after the material is presented. This is particularly true in Chapters 3, 6, 7, and 9. • Numerous new historical notes have been added, primarily in the margins where they can be considered independent of the text material. Much of the current material used in Numerical Analysis was developed in middle of the 20th century, and students should be aware that mathematical discoveries are ongoing. • The bibliographic material has been updated to reflect new editions of books that we reference. New sources have been added that were not previously available. As always with our revisions, every sentence was examined to determine if it was phrased in a manner that best relates what is described. Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it