Leseprobe
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Spectra and Pseudospectra
Lloyd N. Trefethen, Mark Embree
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in.
This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.
Kundenbewertungen
Wave packet, Markov chain, Linear stability, Special case, Big O notation, Companion matrix, Absolute continuity, Reynolds number, Sparse matrix, Series expansion, Free parameter, Stability theory, Asymptotic expansion, ARPACK, Hermite polynomials, Gaussian quadrature, Linear map, Accuracy and precision, Transformation matrix, Unbounded operator, Triangular matrix, Length scale, Norm (mathematics), Krylov subspace, Truncation error (numerical integration), Normal distribution, Singular value, Hessenberg matrix, Numerical range, Unit disk, WKB approximation, Computation, Condition number, Normal operator, Lipschitz continuity, Circular law, Perturbation theory (quantum mechanics), Eigenvalues and eigenvectors, Generalized minimal residual method, Rate of convergence, Stationary distribution, Equation, Stiff equation, Random matrix, Kronecker delta, Inverse iteration, Lanczos algorithm, Random Fibonacci sequence, Dirac delta function, Machine epsilon, Toeplitz matrix, Identity matrix, Nilpotent matrix, Complex plane, Approximation theory, Discretization, Successive over-relaxation, Bounded operator, Theorem, Infimum and supremum, Arnoldi iteration, Arbitrarily large, Lax equivalence theorem, Rayleigh quotient iteration, N-vector, Heavy-tailed distribution, Trapezoidal rule, Power iteration, Eigenfunction, Polynomial