Spectra and Pseudospectra (eBook)

The Behavior of Nonnormal Matrices and Operators

Mark Embree, Lloyd N. Trefethen (Autoren)

eBook Download: PDF

2020
624 Seiten
Princeton University Press (Verlag)
978-0-691-21310-1 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 26.5.2020
• Zusatzinfo: 289 line illus. 5 tables.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Schlagworte: absolute continuity • Accuracy and precision • adjoint operator • algorithm • Approximation Theory • Arbitrarily large • Arnoldi iteration • ARPACK • asymptotic expansion • Big O notation • Boundary conditions • Boundary value problem • bounded operator • circulant matrix • Circular law • Companion matrix • Complex normal distribution • complex plane • Computation • Condition number • Conjugate transpose • continuous function • Control Theory • Diagonalization • Dirac delta function • discretization • Dissipative operator • Eigenfunction • Eigenvalue algorithm • Eigenvalues and Eigenvectors • EigTool • Equation • Euler–Mascheroni constant • Forcing (recursion theory) • Free parameter • Fresnel number • fundamental solution • Gaussian quadrature • Generalized minimal residual method • Group velocity • Heavy-tailed distribution • Hermite Polynomials • hessenberg matrix • hilbert space • Identity matrix • Infimum and supremum • Initial Value Problem • Integration by parts • Invariant subspace • Inverse iteration • Iterative Method • Jordan block • Kronecker delta • Krylov subspace • Lanczos algorithm • Lanczos iteration • Lax equivalence theorem • length scale • Linear dynamical system • Linear map • linear stability • Lipschitz continuity • logarithmic norm • Lyapunov exponent • Machine epsilon • Markov Chain • Mathematical Optimization • MATLAB • Maxima and minima • microlocal analysis • Nilpotent matrix • nonlinear system • nonnormality • Normal distribution • Normal Operator • Norm (mathematics) • Numerical range • N-vector • partial differential equation • Partial fraction decomposition • Perturbation theory (quantum mechanics) • Phase velocity • polynomial • Power iteration • Preconditioner • pseudoeigenvector • Pseudospectrum • Pseudo-zero set • QR decomposition • quantum mechanics • Random Fibonacci sequence • random matrix • Rate of Convergence • Rayleigh quotient iteration • Reynolds Number • Schur decomposition • Semigroup • Series expansion • Shift operator • Singular value • Skew-symmetric matrix • Sparse matrix • Special case • spectral method • spectral theory • Stability Theory • stationary distribution • Stiff equation • Successive over-relaxation • Theorem • Time Scales • Toeplitz Matrix • transformation matrix • Trapezoidal rule • Triangular Matrix • Truncation error (numerical integration) • unbounded operator • Unit disk • Upper and lower bounds • Upper half-plane • Variable coefficients • Vibration • Wave Packet • WKB approximation • Zworski, Maciej
• ISBN-10: 0-691-21310-0 / 0691213100
• ISBN-13: 978-0-691-21310-1 / 9780691213101