Numerical Mathematics

Häftad, Engelska, 1991

689 kr

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This English translation of the highly successful German textbook Numerische Mathematik covers the usual classical topics of numerical analysis, and also includes an up-to-date treatment of both splines and linear optimization methods. The text is designed to be used in a first course in numerical analysis at the upper division undergraduate level or at the beginning graduate level. It features a careful balance between mathematical rigor and numerical insight and includes many worked out numerical examples. Each section concludes with an extensive set of exercises which instructors should find useful in helping students to master the material. Moreover, the authors have also provided carefully researched historical notes which will be of particular interest to experts as well as students.

Produktinformation

Utgivningsdatum1991-01-09
Mått155 x 235 x 24 mm
Vikt663 g
FormatHäftad
SpråkEngelska
SerieUndergraduate Texts in Mathematics
Antal sidor425
Upplaga1991
FörlagSpringer-Verlag New York Inc.
ISBN9780387974941
ÖversättareSchumaker, Larry L.

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Beräkning och matematisk analys inom Naturvetenskap och teknik

1 Computing.- §1. Numbers and Their Representation.- §2. Floating Point Arithmetic.- §3. Error Analysis.- §4. Algorithms.- 2. Linear Systems of Equations.- §1. Gauss Elimination.- §2. The Cholesky Decomposition.- §3. The QR Decomposition of Householder.- §4. Vector Norms and Norms of Matrices.- §5. Error Bounds.- §6. III-Conditioned Problems.- 3. Eigenvalues.- §1. Reduction to Tridiagonal or Hessenberg Form.- §2. The Jacobi Rotation and Eigenvalue Estimates.- §3. The Power Method.- §4. The QR Algorithm.- 4. Approximation.- §1. Preliminaries.- §2. The Approximation Theorems of Weierstrass.- §3. The General Approximation Problem.- §4. Uniform Approximation.- §5. Approximation in Pre-Hilbert Spaces.- §6. The Method of Least Squares.- 5. Interpolation.- §1. The Interpolation Problem.- §2. Interpolation Methods and Remainders.- §3. Equidistant Interpolation Points.- §4. Convergence of Interpolating Polynomials.- §5. More on Interpolation.- §6. Multidimensional Interpolation.- 6. Splines.- §1. Polynomial Splines.- §2. Interpolating Splines.- §3. B-splines.- §4. Computing Interpolating Splines.- §5. Error Bounds and Spline Approximation.- §6. Multidimensional Splines.- 7. Integration.- §1. Interpolatory Quadrature.- §2. Extrapolation.- §3. Gauss Quadrature.- §4. Special Quadrature Methods.- §5. Optimality and Convergence.- §6. Multidimensional Integration.- 8. Iteration.- §1. The General Iteration Method.- §2. Newton’s Method.- §3. Iterative Solution of Linear Systems of Equations.- §4. More on Convergence.- 9. Linear. Optimization.- §1. Introductory Examples and the General Problem.- §2. Polyhedra.- §3. The Simplex Method.- §4. Complexity Analysis.- References.- Symbols.