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Numerical Analysis by L. Ridgway Scott


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Numerical Analysis written by L. Ridgway Scott . This is an other book of mathematics cover the following topics.

  • Numerical Algorithms
    Finding roots, Analyzing Heron’s algorithm, Where to start, An unstable algorithm, General roots: effects of floating-point, Exercises, Solutions

  • Nonlinear Equations
    Fixed-point iteration, Particular methods, Complex roots, Error propagation, More reading, Exercises, Solutions

  • Linear Systems
    Gaussian elimination, Factorization, Triangular matrices, Pivoting, More reading, Exercises, Solutions

  • Direct Solvers
    Direct factorization, Caution about factorization, Banded matrices, More reading, Exercises, Solution

  • Vector Spaces
    Normed vector spaces, Proving the triangle inequality, Relations between norms, Inner-product spaces, More reading, Exercises, Solutions

  • Operators
    Operators, Schur decomposition, Convergent matrices, Powers of matrices, Exercises, Solutions

  • Nonlinear Systems
    Functional iteration for systems, Newton’s method, Limiting behavior of Newton’s method, Mixing solvers, More reading, Exercises, Solutions

  • Iterative Methods
    Stationary iterative methods, General splittings, Necessary conditions for convergence, More reading, Exercises, Solutions

  • Conjugate Gradients
    Minimization methods, Conjugate Gradient iteration, Optimal approximation of CG, Comparing iterative solvers, More reading, Exercises, Solutions

  • Polynomial Interpolation
    Local approximation: Taylor’s theorem, Distributed approximation: interpolation, Norms in infinite-dimensional spaces, More reading, Exercises, Solutions

  • Chebyshev and Hermite Interpolation
    Error term ω, Chebyshev basis functions, Lebesgue function, Generalized interpolation, More reading, Exercises, Solutions

  • Approximation Theory
    Best approximation by polynomials, Weierstrass and Bernstein, Least squares, Piecewise polynomial approximation, Adaptive approximation, More reading, Exercises, Solutions

  • Numerical Quadrature
    Interpolatory quadrature, Peano kernel theorem, Gregorie-Euler-Maclaurin formulas, Other quadrature rules, More reading, Exercises, Solutions
  • Eigenvalue Problems
    Eigenvalue examples, Gershgorin’s theorem, Solving separately, How not to eigen, Reduction to Hessenberg form, More reading, Exercises, Solution

  • Eigenvalue Algorithms
    Power method, Inverse iteration, Singular value decomposition, Comparing factorizations, More reading, Exercises, Solutions

  • Ordinary Differential Equations
    Basic theory of ODEs, Existence and uniqueness of solutions, Basic discretization methods, Convergence of discretization methods, More reading, Exercises, Solutions

  • Higher-order ODE Discretization Methods
    Higher-order discretization, Convergence conditions, Backward differentiation formulas, More reading, Exercises, Solutions

  • Floating Point
    Floating-point arithmetic, Errors in solving systems, More reading, Exercises, Solutions

  • Notation
  • Bibliography
  • Index
  • Download this book

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