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  • 1
    Electronic Resource
    Electronic Resource
    High dimensional polynomial interpolation on sparse grids (2000)
    Springer
    Advances in computational mathematics 12 (2000), S. 273-288 
    Details
    ISSN: 1572-9044
    Keywords: multivariate polynomial interpolation ; sparse grids ; least solution ; universal method ; tractability ; 41A05 ; 41A63 ; 65D05 ; 41A25
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study polynomial interpolation on a d-dimensional cube, where d is large. We suggest to use the least solution at sparse grids with the extrema of the Chebyshev polynomials. The polynomial exactness of this method is almost optimal. Our error bounds show that the method is universal, i.e., almost optimal for many different function spaces. We report on numerical experiments for d = 10 using up to 652 065 interpolation points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018977404843
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  • 2
    Electronic Resource
    Electronic Resource
    Methods of conjugate directions versus quasi-Newton methods (1972)
    Springer
    Mathematical programming 3 (1972), S. 101-116 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract It is shown that algorithms for minimizing an unconstrained functionF(x), x ∈ E n , which are solely methods of conjugate directions can be expected to exhibit only ann or (n−1) step superlinear rate of convergence to an isolated local minimizer. This is contrasted with quasi-Newton methods which can be expected to exhibit every step superlinear convergence. Similar statements about a quadratic rate of convergence hold when a Lipschitz condition is placed on the second derivatives ofF(x).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584978
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A superlinearly convergent method for minimization problems with linear inequality constraints (1973)
    Springer
    Mathematical programming 4 (1973), S. 44-71 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A method is described for minimizing a continuously differentiable functionF(x) ofn variables subject to linear inequality constraints. It can be applied under the same general assumptions as any method of feasible directions. IfF(x) is twice continuously differentiable and the Hessian matrix ofF(x) has certain properties, then the algorithm generates a sequence of points which converges superlinearly to the unique minimizer ofF(x). No computation of secondorder derivatives is required.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584646
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Enhanced transcription of the s-adenosylhomocysteine hydrolase gene precedes Epstein-Barr virus lytic gene activation in ganglioside-stimulated lymphoma cells (2000)
    Springer
    Medical microbiology and immunology 189 (2000), S. 13-18 
    Details
    ISSN: 1432-1831
    Keywords: Key words Differential display ; Gene expression ; Virus reactivation ; Epstein-Barr virus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Stimulation of Epstein-Barr virus (EBV) genome-positive Burkitt lymphoma cells with the ganglioside IV3NeuAc-nLcOse4Cer leads to the induction of cell differentiation processes and activates the EBV lytic viral cycle. In cells of the Burkitt lymphoma line Raji differential expression of host cell genes was analysed in the early phase (150 min) post stimulation with the ganglioside to display the cell activities that precede the activation of the EBV lytic cycle using the differential display reverse transcription-polymerase chain reaction technique. Multiple fragment cDNAs derived from control cells and ganglioside-stimulated cells were amplified using random primers and displayed via polyacrylamide gel electrophoresis. The expression pattern of 8,400 bands was analysed. Eleven differentially expressed fragment cDNAs were reamplified and identified by nucleotide sequencing. Six of these could be identified as coding for proteins that may take part in virus reactivation and differentiation. The most striking finding was the induction of s-adenosylhomocysteine hydrolase (AHCY) expression. The cellular enzyme AHCY plays an important role in transmethylation reactions controlling the replication of several viruses. Thus, an involvement in EBV replication can be suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00008252
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    Paper (German National Licenses)
    Fulltext
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