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  • 1
    Electronic Resource
    Electronic Resource
    Berechnung der Norm der Inversen eines Differentialoperators zweiter Ordnung (1970)
    Springer
    Computing 5 (1970), S. 214-220 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Summary For error estimates and convergence proofs frequently the norm of the inverse of a differential operator is needed. In this paper the norm of the inverse of a second order operator is bounded from above by a finite difference method. At the same time a sufficient criterion for the existence of the inverse is given.
    Notes: Zusammenfassung Zu Fehlerabschätzungen und Konvergenzuntersuchungen wird häufig die Norm der Inversen eines Differentialoperators benötigt. In dieser Arbeit werden für die Norm der Inversen eines Differentialoperators zweiter Ordnung mit Hilfe des Differenzenverfahrens obere Schranken berechnet. Gleichzeitig ergibt sich ein hinreichendes Kriterium für die Existenz der Inversen.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02248022
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    Paper (German National Licenses)
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  • 2
    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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  • 3
    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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  • 4
    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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  • 5
    Electronic Resource
    Electronic Resource
    Das Randwertproblem für eine Klasse singulärer gewöhnlicher Differentialausdrücke (1974)
    Springer
    Aequationes mathematicae 11 (1974), S. 120-120 
    Details
    ISSN: 1420-8903
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01837746
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  • 6
    Electronic Resource
    Electronic Resource
    Das Randwertproblem für eine Klasse singulärer gewöhnlicher Differentialausdrücke (1975)
    Springer
    Aequationes mathematicae 12 (1975), S. 207-228 
    Details
    ISSN: 1420-8903
    Keywords: 34B05 ; 34B25 ; 34B20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01836549
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  • 7
    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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  • 8
    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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  • 9
    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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  • 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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