Mudanças entre as edições de "Análise Numérica"

Edição das 21h11min de 1 de abril de 2009

Esta linha de pesquisa trata da investigação, desenvolvimento, análise e implementação de algoritmos para a resolução de problemas matemáticos. As soluções podem ser algébricas ou numéricas e visam não só a eficiência dos procedimentos, utilizando paralelismo e computação de alto desempenho, mas também a obtenção de novas teorias matemáticas, através das ferramentas da Álgebra Computacional.

[Análise Numérica:Livros]

Jornais

• Acta Numerica
• SIAM Review Journal of Computational Physics
• SIAM Journal on Numerical Analysis
• SIAM Journal on Matrix Analysis & Applications
• SIAM Journal on Scientific Computing
• BIT Numerical Mathematics
• Numerische Mathematik
• IMA Journal of Numerical Analysis
• Mathematics of Computation
• Foundations of Computational Mathematics

Livros

Floating point arithmetic

• M.J. Overton, Numerical Computing and the IEEE Floating Point Standard, SIAM, 2001 (Very readable and systematic presentation.)

See also Chaps. 1 and 2 of the book by N.J. Higham listed below.

Numerical linear algebra

• G.H. Golub & C. Van Loan: Matrix Computations, 3rd ed. Johns Hopkins, 1996 (The most comprehensive introduction to the subject.)
• B.N. Parlett: The Symmetric Eigenvalue Problem, Prentice-Hall, 1980 (Best available account of Lanczos-type methods.)
• L.N. Trefethen & D. Bau: Numerical Linear Algebra, 1997 (General graduate-level text, including Krylov subspace iterations.)
• J.W. Demmel: Applied Numerical Linear Algebra, SIAM, 1997. (Best up-to-date source on recent algorithms such as divide-and-conquer.)
• N.J. Higham: Accuracy and Stability of Numerical Algorithms, SIAM, 1996. (An exceptionally careful and up-to-date study of error analysis.) - 1 -
• A. Greenbaum: Iterative Methods for Solving Linear Systems, SIAM 1997. (Excellent survey of Krylov subspace iterations.)
• H.C. Elman, D.J. Silvester, A.J. Wathen, Finite Elements And Fast Iterative Solvers, Oxford University Press, 2005 (Major new book at the interface of finite elements and matrix iterations.)

Approximation theory

• I. Daubechies: Ten Lectures on Wavelets, SIAM, 1992. (Bestselling introduction to this topic.)
• G. Strang & T. Nguyen: Wavelets and Filter Banks, Wellesley-Cambridge Press, 1996. (Fascinating presentation of wavelets from the linear algebra point of view.)
• P.J. Davies: Interpolation and Approximation, Blaisdell, 1963, reprinted by Dover, 1975. (Old, but extremely well written as an introduction to most aspects of the subject.)
• G. Nürnberger: Approximation by Spline Functions, Springer, 1989.
• M.J.D. Powell: Approximation Theory and Methods, Cambridge, 1981. (Broad introductory text.)
• J.C. Mason and D.C. Handscomb: Chebyshev Polynomials, Chapman & Hall, 2003.

Optimisation and solution of algebraic equations

• J.E. Dennis & R.B. Schnabel: Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, 1983. (Excellent textbook introduction to quasi-Newton methods, including systems of equations as well as optimisation.)
• R. Fletcher: Practical Methods of Optimisation, Wiley, 1987. (Very good general account of methods in this area, with strong practical bias.)
• S. Wright: Primal-Dual Interior Methods, SIAM 1996 (Exceptionally well written introduction to primal-dual methods in mathematical programming.)
• J. Nocedal and S.J. Wright: Numerical Optimization, 2nd ed., Springer, 2006. (The leading general text.)

Applied functional analysis

• V.C.L. Hutson & J. S. Pym: Applications of Functional Analysis and Operator Theory, Academic Press, 1980. (Introductory.)
• E. Kreyszig: Introduction to Functional Analysis and its Applications, Wiley, 1978. (Introductory.)
• A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983. (Advanced.)
• W. Rudin: Functional Analysis, McGraw-Hill, 1973. (Advanced.) - 2 -
• R.E. Showalter: Hilbert Space Methods for Partial Differential Equations, Pitman, 1977. (Introductory.)
• P.D. Lax: Functional Analysis, Wiley, 2002.

Mathematical Analysis and Complex Analysis

• R. Adams: Sobolev Space, Academic Press, 1975. (Advanced.)
• C.M. Bender & S. A. Orszag: Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, 1978. (Classic book on ODES, asymptotics, and much more.)
• A.N. Kolmogorov & S.V. Fomin: Introductory Real Analysis, Dover, 1970. (Introductory)
• W. Rudin: Real and Complex Analysis, McGraw-Hill, 1977. (Introductory but challenging.)
• E.H. Lieb and M. Loss, Analysis, AMS, 1997. (Very nice introductory text.)
• J. Jost: Postmodern Analysis, Springer, 2003 (Excellent introductory text.)
• L.V. Ahlfors, Complex Analysis: An introduction to the theory of analytic functions of one complex variable, McGraw-Hill, 1966.
• H.A. Priestley, Introduction to Complex Analysis, Oxford University Press, 2003.

Ordinary differential equations (theory and numerical solution)

• G. Birkhoff & G.-C. Rota: Ordinary Differential Equations, Ginn, 1962
• J.C. Butcher: Numerical Analysis of Ordinary Differential Equations, Wiley, 1985. (Extensive advanced treatment.)
• E. Hairer, S.P. Norsett & G. Wanner: Solving Ordinary Differential Equations I: Nonstiff Problems, Springer, 2nd rev. ed. 1993, Corr. 2nd printing, 2000. (Delightfully readable advanced account, full of personality.)
• E. Hairer & G. Wanner: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer, 2nd rev. ed. 1996. 3rd printing, 2004. (Second volume of above.)
• H. B. Keller: Numerical Solution of Two-Point Boundary-Value Problems, SIAM, 1976. (Brief but lucid.)
• J. D. Lambert: Numerical Methods for Ordinary Differential Equations: The Initial Value Problem (2nd ed.), Wiley, 1991. (A standard reference.)
• L. F. Shampine: Numerical Solution of Ordinary Differential Equations, Chapman & Hall, 1994. (Includes many practical illustrations.)
• U.M. Ascher and L.R. Petzold: Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, 1998. (Accessible text including DAE’S.) - 3 -

Partial differential equations - Theory

• F. John: Partial Differential Equations, Springer, 4th rev. ed. 1991. (Outstanding introduction.)
• R. Courant & D. Hilbert: Methods of Mathematical Physics, I (1935), II (1962), Interscience. (Old, but well written as an introduction to partial differential equations of mathematical physics.)
• G. Folland: Introduction to Partial Differential Equations, Princeton, 2nd ed. 1995. (Very elegant introduction.)
• P.R. Garabedian: Partial Differential Equations, Wiley, 1964. (Classic.)
• D. Gilbarg & N.S. Trudinger: Elliptic Partial Differential Equations of Second Order, Springer, 1977. (Advanced.)
• M.E. Taylor: Partial Differential equations: Basic Theory, Springer, 1996. (Very nice textbook by the author of “the” multivolume treatise on PDE.)
• L.C. Evans: Partial Differential Equations, AMS, 1998. (Excellent textbook, especially good on nonlinear PDE.)
• H.O. Kreiss & J. Lorenz: Initial Boundary Value Problems and the Navier-Stokes Equations, Academic Press, 1989.
• J. Smoller: Shock Waves and Reaction-Diffusion Equations, Springer, 1983. (Introductory.)

Partial differential equations - Finite difference and spectral methods

• R.J. LeVeque: Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, 2007.
• B. Fornberg: A Practical Guide to Pseudospectral Methods, Cambridge University Press, 1996.
• B. Gustaffson, H.-O. Kreiss & J. Oliger: Time Dependent Problems and Difference Methods, Wiley, 1995.
• R.D. Richtmeyer & K. W. Morton: Difference Methods for Initial-Value Problems, (2nd ed.), Krieger, 1994 (a classic)
• L.N. Trefethen: Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, freely available online. (Trefethen’s text from courses taught at MIT and Cornell.)
• L.N. Trefethen: Spectral Methods in MATLAB, SIAM, 2000. (Basis of our MSc course.)

Partial differential equations - Finite element methods

• S.C. Brenner and L.R. Scott: The Mathematical Theory of Finite Element Methods, Springer, 2nd edition, 2002.
• D.Braess: Finite Elements, Cambridge University Press, 2001. (A very accessible account of the theory of finite element methods.)
• P.G. Ciarlet: The Finite Element Method for Elliptic Problems, North-Holland, 1978. (Difficult to find a copy!)
• C. Johnson: Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge, 1987. (Introductory.)
• G. Strang & G.J. Fix: An Analysis of the finite Element Method, Prentice-Hall, 1973.

Fluid dynamics - Theoretical

• D.A. Anderson: Modern Compressible Flow, McGraw-Hill, 2nd ed., 1990. (A modern treatment, very readable.)
• G.K. Batchelor: An Introduction to Fluid Dynamics, Cambridge, 1970. (Classic, incompressible flow.)
• T. Cebeci & P. Bradshaw: Momentum Transfer in Boundary Layers, McGraw-Hill, 1977. (Theory and computation of boundary layers.)
• H.W. Liepmann & A. Roshko: Elements of Gas Dynamics, Wiley, 1957. (Classic.)
• I.J. Sobey: Introduction to Interactive Boundary Layer Theory, OUP, 2000.

Fluid dynamics - Computational

• D.A. Anderson, J.C. Tannehill & R.A. Pletcher: Computational Fluid Mechanics and Heat Transfer, McGraw-Hill, 1984. (Good introductory book.)
• C. Hirsch: Numerical Computation of Internal and External Flows 1: Fundamentals of Numerical Discretisation, Wiley 1989.
• C. Hirsch: Numerical Computation of Internal and External Flows 2: Computational Methods for Inviscid and Viscous Flows, Wiley 1990.
• R.J. LeVeque: Finite volume Methods for Hyperbolic Problems, Cambridge, 2002
• R.J. LeVeque: Numerical Methods for Conservation Laws, Birkhäuser. (Earlier, shorter introductory text, very readable.)
• R. Peyret & T.D. Taylor: Computational Methods for Fluid Flow, Springer, 1983