A useful resource for graduate students in numerical analysis, this text features a clear and comprehensive exposition on all important topics, simple notation, and an emphasis on theory over implementation. Including classroom-tested problems ranging from simple verification to qualifying exam-level problems.
A useful resource for graduate students in numerical analysis, this text features a clear and comprehensive exposition on all important topics, simple notation, and an emphasis on theory over implementation. Including classroom-tested problems ranging from simple verification to qualifying exam-level problems.
Abner J. Salgado is Professor of Mathematics at the University of Tennessee, Knoxville. He obtained his PhD in Mathematics in 2010 from Texas A&M University. His main area of research is the numerical analysis of nonlinear partial differential equations, and related questions.
Inhaltsangabe
Part I. Numerical Linear Algebra: 1. Linear operators and matrices 2. The singular value decomposition 3. Systems of linear equations 4. Norms and matrix conditioning 5. Linear least squares problem 6. Linear iterative methods 7. Variational and Krylov subspace methods 8. Eigenvalue problems Part II. Constructive Approximation Theory: 9. Polynomial interpolation 10. Minimax polynomial approximation 11. Polynomial least squares approximation 12. Fourier series 13. Trigonometric interpolation and the Fast Fourier Transform 14. Numerical quadrature Part III. Nonlinear Equations and Optimization: 15. Solution of nonlinear equations 16. Convex optimization Part IV. Initial Value Problems for Ordinary Di fferential Equations: 17. Initial value problems for ordinary diff erential equations 18. Single-step methods 19. Runge¿Kutta methods 20. Linear multi-step methods 21. Sti ff systems of ordinary diff erential equations and linear stability 22. Galerkin methods for initial value problems Part V. Boundary and Initial Boundary Value Problems: 23. Boundary and initial boundary value problems for partial di fferential equations 24. Finite diff erence methods for elliptic problems 25. Finite element methods for elliptic problems 26. Spectral and pseudo-spectral methods for periodic elliptic equations 27. Collocation methods for elliptic equations 28. Finite di fference methods for parabolic problems 29. Finite diff erence methods for hyperbolic problems Appendix A. Linear algebra review Appendix B. Basic analysis review Appendix C. Banach fixed point theorem Appendix D. A (petting) zoo of function spaces References Index.
Part I. Numerical Linear Algebra: 1. Linear operators and matrices 2. The singular value decomposition 3. Systems of linear equations 4. Norms and matrix conditioning 5. Linear least squares problem 6. Linear iterative methods 7. Variational and Krylov subspace methods 8. Eigenvalue problems Part II. Constructive Approximation Theory: 9. Polynomial interpolation 10. Minimax polynomial approximation 11. Polynomial least squares approximation 12. Fourier series 13. Trigonometric interpolation and the Fast Fourier Transform 14. Numerical quadrature Part III. Nonlinear Equations and Optimization: 15. Solution of nonlinear equations 16. Convex optimization Part IV. Initial Value Problems for Ordinary Di fferential Equations: 17. Initial value problems for ordinary diff erential equations 18. Single-step methods 19. Runge¿Kutta methods 20. Linear multi-step methods 21. Sti ff systems of ordinary diff erential equations and linear stability 22. Galerkin methods for initial value problems Part V. Boundary and Initial Boundary Value Problems: 23. Boundary and initial boundary value problems for partial di fferential equations 24. Finite diff erence methods for elliptic problems 25. Finite element methods for elliptic problems 26. Spectral and pseudo-spectral methods for periodic elliptic equations 27. Collocation methods for elliptic equations 28. Finite di fference methods for parabolic problems 29. Finite diff erence methods for hyperbolic problems Appendix A. Linear algebra review Appendix B. Basic analysis review Appendix C. Banach fixed point theorem Appendix D. A (petting) zoo of function spaces References Index.
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