# Numerical Linear Algebra

## Lloyd N. Trefethen; David Bau III

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This is a concise, insightful introduction to the field of numerical linear algebra. The clarity and eloquence of the presentation make it popular with teachers and students alike. The text aims to expand the reader's view of the field and to present standard material in a novel way. All of the most important topics in the field are covered with a fresh perspective, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability. Presentation is in the form of 40 lectures, which each focus on one or two central ideas. The unity between topics is emphasized throughout, with no risk of getting lost in details and technicalities. The book breaks with tradition by beginning with the QR factorization - an important and fresh idea for students, and the thread that connects most of the algorithms of numerical linear algebra.

Contents: Preface; Acknowledgments; Part I: Fundamentals. Lecture 1: Matrix-Vector Multiplication; Lecture 2: Orthogonal Vectors and Matrices; Lecture 3: Norms; Lecture 4: The Singular Value Decomposition; Lecture 5: More on the SVD; Part II: QR Factorization and Least Squares. Lecture 6: Projectors; Lecture 7: QR Factorization; Lecture 8: Gram-Schmidt Orthogonalization; Lecture 9: MATLAB; Lecture 10: Householder Triangularization; Lecture 11: Least Squares Problems; Part III: Conditioning and Stability. Lecture 12: Conditioning and Condition Numbers; Lecture 13: Floating Point Arithmetic; Lecture 14: Stability; Lecture 15: More on Stability; Lecture 16: Stability of Householder Triangularization; Lecture 17: Stability of Back Substitution; Lecture 18: Conditioning of Least Squares Problems; Lecture 19: Stability of Least Squares Algorithms; Part IV: Systems of Equations. Lecture 20: Gaussian Elimination; Lecture 21: Pivoting; Lecture 22: Stability of Gaussian Elimination; Lecture 23: Cholesky Factorization; Part V: Eigenvalues. Lecture 24: Eigenvalue Problems; Lecture 25: Overview of Eigenvalue Algorithms; Lecture 26: Reduction to Hessenberg or Tridiagonal Form; Lecture 27: Rayleigh Quotient, Inverse Iteration; Lecture 28: QR Algorithm without Shifts; Lecture 29: QR Algorithm with Shifts; Lecture 30: Other Eigenvalue Algorithms; Lecture 31: Computing the SVD; Part VI: Iterative Methods. Lecture 32: Overview of Iterative Methods; Lecture 33: The Arnoldi Iteration; Lecture 34: How Arnoldi Locates Eigenvalues; Lecture 35: GMRES; Lecture 36: The Lanczos Iteration; Lecture 37: From Lanczos to Gauss Quadrature; Lecture 38: Conjugate Gradients; Lecture 39: Biorthogonalization Methods; Lecture 40: Preconditioning; Appendix: The Definition of Numerical Analysis; Notes; Bibliography; Index.

Audience: Written on the graduate or advanced undergraduate level, this book can be used widely for teaching. Professors looking for an elegant presentation of the topic will find it an excellent teaching tool for a one-semester graduate or advanced undergraduate course. A major contribution to the applied mathematics literature, most researchers in the field will consider it a necessary addition to their personal collections.

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Book Description:

This is a concise, insightful introduction to the field of numerical linear algebra. The authors' clear, inviting style and evident love of the field, along with their eloquent presentation of the most fundamental ideas in numerical linear algebra, make it popular with teachers and students alike.

Lloyd N. Trefethen is a Professor of Computer Science at Cornell University. Starting October 1, 1997, he will be the Professor of Numerical Analysis at Oxford University in England. He has won teaching awards at both MIT and Cornell. In addition to editorial positions on such journals as SIAM Journal on Numerical Analysis, Journal of Computational and Applied Mathematics, Numerische Mathematik, and SIAM Review, he has been an invited lecturer at two dozen international conferences. While at Cornell, David Bau was a student of Trefethen. He is currently a Software Engineer at Google Inc., where he helped develop Google Talk, Google's IM and VOIP service.

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## 1.Numerical Linear Algebra

Editorial: Society for Industrial & Applied Mathematics,U.S.
ISBN 10: 0898713617 ISBN 13: 9780898713619
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THE SAINT BOOKSTORE
(Southport, Reino Unido)
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Descripción Society for Industrial & Applied Mathematics,U.S. Paperback. Estado de conservación: new. BRAND NEW, Numerical Linear Algebra, Lloyd N. Trefethen, David Bau, This is a concise, insightful introduction to the field of numerical linear algebra. The clarity and eloquence of the presentation make it popular with teachers and students alike. The text aims to expand the reader's view of the field and to present standard material in a novel way. All of the most important topics in the field are covered with a fresh perspective, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability. Presentation is in the form of 40 lectures, which each focus on one or two central ideas. The unity between topics is emphasized throughout, with no risk of getting lost in details and technicalities. The book breaks with tradition by beginning with the QR factorization - an important and fresh idea for students, and the thread that connects most of the algorithms of numerical linear algebra. Nº de ref. de la librería B9780898713619

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## 2.Numerical Linear Algebra

ISBN 10: 0898713617 ISBN 13: 9780898713619
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Descripción Estado de conservación: New. Depending on your location, this item may ship from the US or UK. Nº de ref. de la librería 97808987136190000000

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## 3.Numerical Linear Algebra (Paperback)

Editorial: Society for Industrial Applied Mathematics,U.S., United States (2016)
ISBN 10: 0898713617 ISBN 13: 9780898713619
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The Book Depository
(London, Reino Unido)
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Descripción Society for Industrial Applied Mathematics,U.S., United States, 2016. Paperback. Estado de conservación: New. Language: English . Brand New Book. This is a concise, insightful introduction to the field of numerical linear algebra. The clarity and eloquence of the presentation make it popular with teachers and students alike. The text aims to expand the reader s view of the field and to present standard material in a novel way. All of the most important topics in the field are covered with a fresh perspective, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability. Presentation is in the form of 40 lectures, which each focus on one or two central ideas. The unity between topics is emphasized throughout, with no risk of getting lost in details and technicalities. The book breaks with tradition by beginning with the QR factorization - an important and fresh idea for students, and the thread that connects most of the algorithms of numerical linear algebra. Nº de ref. de la librería AAN9780898713619

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## 4.Numerical Linear Algebra (Paperback)

Editorial: Society for Industrial Applied Mathematics,U.S., United States (2016)
ISBN 10: 0898713617 ISBN 13: 9780898713619
Librería
The Book Depository US
(London, Reino Unido)
Valoración

Descripción Society for Industrial Applied Mathematics,U.S., United States, 2016. Paperback. Estado de conservación: New. Language: English . Brand New Book. This is a concise, insightful introduction to the field of numerical linear algebra. The clarity and eloquence of the presentation make it popular with teachers and students alike. The text aims to expand the reader s view of the field and to present standard material in a novel way. All of the most important topics in the field are covered with a fresh perspective, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability. Presentation is in the form of 40 lectures, which each focus on one or two central ideas. The unity between topics is emphasized throughout, with no risk of getting lost in details and technicalities. The book breaks with tradition by beginning with the QR factorization - an important and fresh idea for students, and the thread that connects most of the algorithms of numerical linear algebra. Nº de ref. de la librería AAN9780898713619

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## 5.Numerical Linear Algebra

Editorial: Society for Industrial and Applied Mathematics (1997)
ISBN 10: 0898713617 ISBN 13: 9780898713619
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Books2Anywhere
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Descripción Society for Industrial and Applied Mathematics, 1997. PAP. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería CE-9780898713619

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## 6.Numerical Linear Algebra

Editorial: SIAM: Society for Industrial and Applied Mathematics (1997)
ISBN 10: 0898713617 ISBN 13: 9780898713619
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Ergodebooks
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Descripción SIAM: Society for Industrial and Applied Mathematics, 1997. Paperback. Estado de conservación: New. Nº de ref. de la librería DADAX0898713617

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## 7.NUMERICAL LINEAR ALGEBRA

Editorial: Soc Industrial Applied Maths (1997)
ISBN 10: 0898713617 ISBN 13: 9780898713619
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Descripción Soc Industrial Applied Maths, 1997. Paperback. Estado de conservación: NEW. 9780898713619 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE01294580

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## 8.Numerical Linear Algebra

Editorial: SIAM: Society for Industrial and Applied Mathematics (1997)
ISBN 10: 0898713617 ISBN 13: 9780898713619
Nuevos Paperback Primera edición Cantidad: 1
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Descripción SIAM: Society for Industrial and Applied Mathematics, 1997. Paperback. Estado de conservación: New. book. Nº de ref. de la librería 0898713617

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## 9.Numerical Linear Algebra

Editorial: SIAM: Society for Industrial a (1997)
ISBN 10: 0898713617 ISBN 13: 9780898713619