Jackowski, T. (1990), Complexity of multilinear problems in the worst case setting, J. Complexity 6, 389--408.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....1995) and stochastic differential equations (Revuz and Yor, 1994) In our study of Stieltjes integration, we shall assume that we have partial information about f and g. This means that we are considering a nonlinear integration problem; more precisely, the problem is bilinear in the sense of Jackowski (1990). It is our belief that most of the linear problems arising in IBC have important nonlinear counterparts; this is only one example. In this paper, we shall assume that f has r continuous derivatives and that g (s) is of bounded variation. More precisely, we shall assume that f belongs to the ....

....We compute an approximation to S( f , g] by first evaluating information about f and g, and then using this information in an algorithm. For our problem, we will compute standard information N( f , g] f (x 1 ) f (x m ) g(t 1 ) g(t n m ) 2. 2) 4 about [ f , g] By Jackowski (1990, Theorem 3.2.4) there is essentially no loss of generality in assuming that the information is nonadaptive, i.e. the points 0 # x 1 x 2 x m # 1 and 0 # t 1 t 2 t n m # 1, are independent of f and g. We obtain an approximation U ( f , g] to the solution S( f , g] ....

Jackowski, T. (1990), Complexity of multilinear problems in the worst case setting, J. Complexity 6, 389--408.

....1995) and stochastic differential equations (Revuz and Yor, 1994) In our study of Stieltjes integration, we shall assume that we have partial information about f and g. This means that we are considering a nonlinear integration problem; more precisely, the problem is bilinear in the sense of Jackowski (1990). It is our belief that most of the linear problems arising in IBC have important nonlinear counterparts; this is only one example. In this paper, we shall assume that f has r continuous derivatives and that g (s) is of bounded variation. More precisely, we shall assume that f belongs to the ....

....F Theta G. We compute an approximation to S( f; g] by first evaluating information about f and g, and then using this information in an algorithm. For our problem, we will compute standard information N ( f; g] f(x 1 ) f(xm ) g(t 1 ) g(t n Gammam ) 2. 2) about [f; g] By Jackowski (1990, Theorem 3.2.4) there is essentially no loss of generality in assuming that the information is nonadaptive, i.e. the points 0 x 1 x 2 Delta Delta Delta xm 1 and 0 t 1 t 2 Delta Delta Delta t n Gammam 1; are independent of f and g. We obtain an approximation U ( f; g] to ....

Jackowski, T. (1990), Complexity of multilinear problems in the worst case setting, J. Complexity 6, 389--408.

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