Numerical Linear Algebra
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Description: 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.
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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
Copyright year: 1997
Publisher: Society for Industrial and Applied Mathematics
Size: 7.25" wide x 10.25" long x 0.75" tall
|Orthogonal vectors and matrices|
|The singular value decomposition|
|More on the SVD|
|QR Factorization and Least Squares:|
|Least squares problems|
|Conditioning and Stability:|
|Conditioning and condition numbers|
|Floating point arithmetic|
|More on stability|
|Stability of householder triangularization|
|Stability of back substitution|
|Conditioning of least squares problems|
|Stability of least squares algorithms|
|Systems of Equations:|
|Stability of Gaussian elimination|
|Overview of Eigenvalue algorithms|
|Reduction to Hessenberg or tridiagonal form|
|Rayleigh quotient, inverse iteration|
|QR algorithm without shifts|
|QR algorithm with shifts|
|Other Eigenvalue algorithms|
|Computing the SVD|
|Overview of iterative methods|
|The Arnoldi iteration|
|How Arnoldi locates Eigenvalues|
|The Lanczos iteration|
|From Lanczos to Gauss quadrature|