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BL
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| Record Number
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838722
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| Main Entry
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Fröberg, Carl Erik.
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| Title & Author
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Numerical mathematics : : theory and computer applications /\ Carl-Erik Fröberg.
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| Publication Statement
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Menlo Park, Calif. :: Benjamin/Cummings Pub. Co.,, 1985.
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| Page. NO
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xi, 436 pages :: illustrations ;; 25 cm
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| ISBN
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0805325301
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: 9780805325300
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| Notes
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Revised edition of: Introduction to numerical analysis. 2nd ed. 1969.
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| Bibliographies/Indexes
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Includes bibliographical references (pages 424-426) and index.
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| Contents
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I. Mathematical introduction. 1. Numerical computation. Representation of numbers -- The origin and growth of errors -- Numerical cancellation -- Algorithms and complexity -- Use of computers. 2. Vectors and matrices. Vectors -- Matrices -- Eigenvalues and eigenvectors -- Matrix norms -- Matrix functions -- Localization of eigenvalues -- Normal forms -- Rectangular matrices. 3. Series expansions. Power series -- Generating functions -- Asymptotic series -- Fourier series -- Bernoulli numbers and Bernoulli polynomials -- Continued fractions. 4. Orthoganal functions. General concepts -- Polynomials: orthoganal; Legendre; Laguerre; Hermite; Chebyshev. 5. Linear operations. General properties -- Special operators -- Representation with differences -- Factorials and stirling numbers. 6. Difference equations. General concepts -- Linear, homogeneous difference equations -- Differences of elementary functions.
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Partial difference equations. 7. Special functions. Analytic functions and complex integration -- The gamma function -- The beta function -- Some functions defined defined by definite integrals -- The Riemann zeta function -- Bessel functions -- Spherical harmonics. 8. Laplace transformation. Basic theory -- Laplace transforms of some special functions. 9. Calculus of variations. II. Equations. Gaussian elimination -- Error analysis -- Overdetermined systems of equations -- Iterative methods -- Gradient methods. 11. Nonlinear equations and systems of equations. Equations in one variable -- Horner's scheme -- Interpolation methods for real roots -- Fixed-point methods -- Laguerre's method -- Systems of nonlinear equations -- Minimization methods. 12. Algebraic eigenvalue problems. Iteravive methods -- Transformation methods. 13. Linear programming. The simplex method -- The transportation problem.
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Quadratic, integer, and dynamic programming. III. Approximation. 14. Interpolation. Polynomial interpolation -- Devided differences -- Interpolation by use of differences -- Extrapolation -- Special features. 15. Function representation and curve fitting. Least-squares polynomial approximation -- Trigonometric interpolation -- The fast Fourier transform -- Approximation with: trigonometric functions; exponential functions; Chebyshev polynomials -- Spline approximation -- Rational approximations. 16. The Monte Carlo method. Random numbers -- Random walks -- Computation of definite integrals -- Simulation. IV. Integration and summation. 17. Numerical integration. General rules -- Methods based on equidistant node points -- Formulas of Gauss type -- Multiple integrals. 18. Summation. Sums of factorials and powers -- Euler-McLaurin's summation formula -- Stirling's formula -- Euler's transformation and alternating series.
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Summation by use of Riemann's zeta function. V. Differential and integral equations. 19. Ordinary differential equations. Existeence of solutions -- Euler's method -- Taylor series expansion -- Runge-Kutta (RK) methods -- Stiff differential equations -- Multi-step methods -- Cowell-Numerov's method -- Systems of firts-order linear differential equations -- Boundary value problems -- Eigenvalue problems. 20. Partial differential equations. Classification -- Hyperbolic equations -- Parabolic equations -- Elliptic equations -- The finite element method (FEM) -- Eigenvalue problems. 2. Integral equations. Classification -- Fredholm's inhomogeneous equation of the second kind -- ... homogeneous ... -- Fredholm's equation of the first kind -- Volterra's equations -- Numerical treatment of integral equations -- Connections between differential and integral equations.
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| Subject
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Numerical analysis-- Data processing.
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Numerical analysis.
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Analyse numérique-- Informatique.
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Analyse numérique.
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Analyse numérique-- Logiciels.
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Analyse numérique.
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Analysis
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Numerical analysis-- Data processing.
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| Subject
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Numerical analysis.
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Numerische Mathematik
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| Dewey Classification
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511
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| LC Classification
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QA297.F6813 1985
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| NLM classification
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MAT 650fstub
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SK 900rvk
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| Added Entry
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Fröberg, Carl Erik.
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