Mudanças entre as edições de "Análise Numérica"

Edição das 21h06min 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.

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.) - 4 - 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