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  • 1
    Call number: M 05.0214
    In: Heidelberger geowissenschaftliche Abhandlungen
    Type of Medium: Monograph available for loan
    Pages: VII, 143 S., 3 Pläne
    ISBN: 3892570159
    Series Statement: Heidelberger geowissenschaftliche Abhandlungen 16
    Note: Heidelberg, Univ., Naturwiss.-Mathematische Gesamtfak., 1987
    Location: Upper compact magazine
    Branch Library: GFZ Library
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  • 2
    Monograph available for loan
    Monograph available for loan
    Berlin [u.a.] : de Gruyter
    Call number: IASS 16.90521
    Type of Medium: Monograph available for loan
    Pages: VIII, 703 S. , graph. Darst.
    ISBN: 9783110312881 , 9783110312959 (electronic)
    Series Statement: Narratologia 35
    Language: German
    Branch Library: IASS Library
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Manuscripta mathematica 32 (1980), S. 263-294 
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this note, we present a general automatic continuity theory for linear mappings between certain topological vector spaces. The theory applies, in particular, to local operators between spaces of functions and distributions, to algebraic homomorphisms between certain topological algebras, and to linear mappings intertwining generalized scalar operators.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Manuscripta mathematica 38 (1982), S. 131-161 
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this article we characterize certain ultradifferential operators by the condition of being local. First, we examine the continuity properties of local linear operators on spaces of ultradifferentiable functions in the sense of Beurling and of Roumieu. Next, a structure theorem for vector-valued ultradistributions with support at the origin is proved. This result leads to a representation theorem for continuous local operators from spaces of ultradifferentiable functions into various spaces of ultradistributions. In combination with the continuity results we thus obtain in many cases the desired characterization.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Manuscripta mathematica 26 (1978), S. 37-61 
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this note, some of the fundamental theorems concerning the automatic continuity of positive linear functionals and positive linear operators (see [9,14,21]) as well as certain uniform boundedness type theorems (see [5,13,15,19]) will be extended to derive various continuity properties of (even discontinuous) sublinear operators from some metrizable topological vector space to some ordered topological vector space.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Mathematische Annalen 240 (1979), S. 251-280 
    ISSN: 1432-1807
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 47 (1985), S. 427-434 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: G.1.3
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In a recent paper, [4], Csordas and Varga have unified and extended earlier theorems, of Varga in [10] and Woźnicki in [11], on the comparison of the asymptotic rates of convergence of two iteration matrices induced by two regular splittings. The main purpose of this note is to show a connection between the Csordas-Varga paper and a paper by Beauwens, [1], in which a comparison theorem is developed for the asymptotic rate of convergence of two nonnegative iteration matrices induced by two splittings which are not necessarily regular. Monotonic norms already used in [1] play an important role in our work here.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 35 (1980), S. 69-79 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Sharpness is shown for three upper bounds for the spectral radii of point S.O.R. iteration matrices resulting from the splitting (i) of a nonsingularH-matrixA into the ‘usual’D−L−U, and (ii) of an hermitian positive definite matrixA intoD−L−U, whereD is hermitian positive definite andL=1/2(A−D+S) withS some skew-hermitian matrix. The first upper bound (which is related to the splitting in (i)) is due to Kahan [6], Apostolatos and Kulisch [1] and Kulisch [7], while the remaining upper bounds (which are related to the splitting in (ii)) are due to Varga [11]. The considerations regarding the first bound yield an answer to a question which, in essence, was recently posed by Professor Ridgway Scott: What is the largest interval in ω, ω≧0, for which the point S.O.R. iterative method is convergent for all strictly diagonally dominant matrices of arbitrary order? The answer is, precisely, the interval (0, 1].
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 57 (1990), S. 85-95 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10, 65F20 ; CR: G 1.3
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Recently Eiermann, Marek, and Niethammer have shown how to applysemiiterative methods to a fixed point systemx=Tx+c which isinconsistent or in whichthe powers of the fixed point operator T have no limit, to obtain iterative methods which converge to some approximate solution to the fixed point system. In view of their results we consider here stipulations on apreconditioning QAx=Qb of the systemAx=b and, separately, on asplitting A=M−N which lead to fixed point systems such that, with the aid of a semiiterative method, the iterative scheme converges to a weighted Moore-Penrose solution to the systemAx=b. We show in several ways that to obtain a meaningful limit point from a semiiterative method requires less restrictions on the splittings or the reconditionings than those which have been required in the classical Picard iterative method (see, e.g., the works of Berman and Plemmons, Berman and Neumann, and Tanabe). We pay special attention to the case when the weighted Moore-Penrose solution which is sought is the minimal norm least squares solution toAx=b.
    Type of Medium: Electronic Resource
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  • 10
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: G1.3
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Ann×n complex matrixB is calledparacontracting if ‖B‖2≦1 and 0≠x∈[N(I-B)]⊥⇒‖Bx‖2〈‖x‖2. We show that a productB=B k B k−1 ...B 1 ofk paracontracting matrices is semiconvergent and give upper bounds on the subdominant eigenvalue ofB in terms of the subdominant singular values of theB i 's and in terms of the angles between certain subspaces. Our results here extend earlier results due to Halperin and due to Smith, Solomon and Wagner. We also determine necessary and sufficient conditions forn numbers in the interval [0, 1] to form the spectrum of a product of two orthogonal projections and hence characterize the subdominant eigenvalue of such a product. In the final part of the paper we apply the upper bounds mentioned earlier to provide an estimate on the subdominant eigenvalue of the SOR iteration matrix ℒω associated with ann×n hermitian positive semidefinite matrixA none of whose diagonal entries vanish.
    Type of Medium: Electronic Resource
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