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  • 13P10  (1)
  • Cognitive Behaviour Therapy  (1)
  • Dual bases  (1)
  • 2000-2004  (1)
  • 1990-1994  (2)
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  • 2000-2004  (1)
  • 1990-1994  (2)
Year
  • 1
    Electronic Resource
    Electronic Resource
    H-bases for polynomial interpolation and system solving (2000)
    Springer
    Advances in computational mathematics 12 (2000), S. 335-362 
    Details
    ISSN: 1572-9044
    Keywords: ideal bases ; Gröbner bases ; multivariate polynomials ; interpolation ; systems of polynomial equations ; 65D05 ; 65H10 ; 13P10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The H-basis concept allows, similarly to the Gröbner basis concept, a reformulation of nonlinear problems in terms of linear algebra. We exhibit parallels of the two concepts, show properties of H-bases, discuss their construction and uniqueness questions, and prove that n polynomials in n variables are, under mild conditions, already H-bases. We apply H-bases to the solution of polynomial systems by the eigenmethod and to multivariate interpolation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018937723499
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Gröbner bases of ideals defined by functionals with an application to ideals of projective points (1993)
    Springer
    Applicable algebra in engineering, communication and computing 4 (1993), S. 103-145 
    Details
    ISSN: 1432-0622
    Keywords: Gröbner bases ; Polynomial ideals ; Dual bases ; Interpolation ; 0-dimensional schemes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics , Technology
    Notes: Abstract In this paper we study 0-dimensional polynomial ideals defined by a dual basis, i.e. as the set of polynomials which are in the kernel of a set of linear morphisms from the polynomial ring to the base field. For such ideals, we give polynomial complexity algorithms to compute a Gröbner basis, generalizing the Buchberger-Möller algorithm for computing a basis of an ideal vanishing at a set of points and the FGLM basis conversion algorithm. As an application to Algebraic Geometry, we show how to compute in polynomial time a minimal basis of an ideal of projective points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01386834
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Prediction of short-term outcome of neurotic-depressive inpatients (1993)
    Springer
    European archives of psychiatry and clinical neuroscience 242 (1993), S. 301-309 
    Details
    ISSN: 1433-8491
    Keywords: Neurotic Depression ; Short-term Outcome ; Predictors ; Cognitive Behaviour Therapy ; Antidepressants
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary A study was carried out involving 134 neurotic-depressive inpatients (according to ICD-9) treated with cognitive behaviour therapy and in a subgroup additionally with antidepressants. Using standardized rating instruments, a large set of potential predictor variables was tested. After cross-validation according to the splithalf technique, only very few of these proved to be suitable as predictors for the main outcome criteria. These predictors included certain aspects of social functioning before index admission, intensity of depressive symptoms at admission and the degree of self-evaluated mood disturbances three weeks after admission. Several predictors known from the literature could not be reproduced in this study, demonstrating the well-known instability of most predictor findings. On the other side, the predictor profile of the neurotic-depressive patients was quite similar to that found in endogenous depressives, a result which might — together with other findings, such as the response of neurotic depressives to antidepressants — question the traditional subclassification of functional depressive states into these subgroups.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02190390
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    Paper (German National Licenses)
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