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  • 1
    Electronic Resource
    Electronic Resource
    Fourier reconstruction in tomography (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 343-353 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 42-04, 65T05 ; CR: σ·1m
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We give an asymptotic error analysis of the Fourier reconstruction algorithm and show that a modified algorithm is asymptotically optimal. We compare the modified algorithm with standard Fourier and with filtered backprojection using a mathematically generated chest phantom.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389583
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Einschließungen für die großen Eigenwerte gewöhnlicher Differentialgleichungen zweiter und vierter Ordnung (1969)
    Springer
    Numerische Mathematik 13 (1969), S. 78-93 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary New asymptotic solutions of linear homogeneous differential equations of second order are given. Using these, the high eigenvalues of two general classes of natural eigenvalue problems are enclosed in intervals, whose length behaves asymptotically like a prescribed negative power of the eigenvalue. Approximations are given for the corresponding eigenfunctions with an error estimate in the Chebyshev sense. The results are in part extended to fourth order problems. Some numerical examples are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02165274
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Numerische Behandlung singulärer Sturm-Liouville-Probleme (1969)
    Springer
    Numerische Mathematik 13 (1969), S. 434-447 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Generalizing the method of Wendroff [9] and using an estimate for the square integral of a normed eigenfunction outside a compact set, bounds are obtained for the eigenvalues of singular Sturm-Liouville problems from a finite difference method. The number of mesh points necessary to obtain. the accuracy ε behaves like ε−½ lnε ifε tends to zero. Some numerical examples are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02163271
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Schranken für die Eigenwerte gewöhnlicher Differentialgleichungen durch Spline-Approximation (1970)
    Springer
    Numerische Mathematik 14 (1970), S. 346-354 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper is concerned with the computation of the eigenvalues of selfadjoint ordinary differential equations by Rayleigh-Ritz methods using splines. It is shown that computable error bounds may be obtained for a large class of such methods. Some numerical examples are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02165590
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Das Differenzenverfahren für singuläre Rand-Eigenwertaufgaben gewöhnlicher Differentialgleichungen (1975)
    Springer
    Numerische Mathematik 23 (1975), S. 387-409 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The boundary value problem for a class of singular second order differential operators is defined. Using the standard three point discretisation for the differential equation and taking care of the limits involved in the boundary conditions in a natural way, finite difference approximations to the boundary value problems are defined and their convergence properties are investigated. The rate of convergence is given in terms of the data. It turns out that for problems of the first kind extrapolation is possible up to an arbitrary order after a suitable change of the independent variable, whereas for problems of the second kind neither theoretical nor numerical results indicate the possibility of extrapolation. Corresponding results hold for the eigenvalue problems. Some numerical examples show that the convergence rates given in the paper are best possible and demonstrate the effect of extrapolation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01437038
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Regularisierung schlecht gestellter Probleme durch Projektionsverfahren (1977)
    Springer
    Numerische Mathematik 28 (1977), S. 329-341 
    Details
    ISSN: 0945-3245
    Keywords: Primary 65 J 05 ; secondary 65 R 05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The numerical solution of ill-posed problems by projection methods is considered. Regularization is carried out simply by choosing an optimal discretization parameter. It is shown by asymptotic estimates and by numerical examples that this kind of regularization is as efficient as the method of Tikhonov and Phillips.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389972
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  • 7
    Electronic Resource
    Electronic Resource
    Eine Erweiterung des Maximumprinzips für den Laplaceschen Operator (1974)
    Springer
    Numerische Mathematik 22 (1974), S. 149-155 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary It is shown that the classical maximum principle holds for continuous functionsu, if Δu taken in the distributional sense is a non-negativ functional. As an application the maximum principle is formulated for continuous functions with piecewiese continuous first and second derivatives. For this case an independend proof is given. Generalizations to parabolic and to more complicated elliptic operators are indicated. Two simple applications to the numerical solution of the Dirichlet problem are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01436729
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Über die punktweise Konvergenz Finiter Elemente (1975)
    Springer
    Numerische Mathematik 25 (1975), S. 67-77 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The solution of the Dirichlet problem for Poissons equation −δu=f in a two dimensional convex polyhedral domain Ω is approximated by the simplest finite element method, where the trial functions are linear in triangles of maximal diameterh. The convergence rate in certain weighted Sobolev spaces is established. It follows that for everyx∈Ω, the rate of convergence inx ish 2−ε with arbitrary small ε〉0, iff∈L 2(Ω) andf bounded in a neighbourhood ofx. This estimate is close to theh 2-accuracy observed in practical calculations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01419529
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    On the inversion of the attenuated Radon transform (1979)
    Springer
    Numerische Mathematik 32 (1979), S. 431-438 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65R05 ; CR ; 5.18
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We given an inversion formula for the attenuated Radon transform $$\bar \omega _L $$ for constant attenuation μ which is accurate up toO(µ 4) We also derive an integral equation of the second kind for the solution ofR μf=g. The implementation of both methods for the inversion ofR μ consists basically of a generalized filtered backprojection algorithm. Numerical examples are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01401046
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Schranken für die Norm der Greenschen Funktion gewöhnlicher Differentialoperatoren (1971)
    Springer
    Numerische Mathematik 17 (1971), S. 402-408 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The paper describes a finite difference method for bounding the norm of the inverse of an ordinary differential operator. Some numerical examples are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01436089
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    Paper (German National Licenses)
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