A. BORODIN AND P. TIWARI, On the decidability of sparse univariate polynomial interpolation, Comput. Complexity, 1 (1991), pp. 67--90.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....sparse representations for various classes of functions such as polynomials, rational functions, and algebraic functions (Grigoriev Karpinski Work supported by NSF grant CCR 9203062 y Work supported by NSF grant CCR 9123666. 1987, Clausen et al. 1988, Ben Or Tiwari 1988, KaltofenLakshman 1988, Borodin Tiwari 1990, Grigoriev KarpinskiSinger 1990,1991a,1991b, Mansour 1992) Sparse interpolation is well recognized as a very useful tool for controlling intermediate expression swell in computer algebra (Zippel 1990, Kaltofen Trager 1990) Sparse polynomials and rational functions can be evaluated quickly and ....

.... 1992) and a different generalized sparse interpolation algorithm that works for a class of bases can be found in (Grigoriev Karpinski Singer 1991b) Computing t sparse shifts and the representation of f(x) in the basis 1; x Gamma ff; x Gamma ff) 2 ; was raised as an open problem in (Borodin Tiwari 1990). Subsequently, the problem was taken up in a recent paper by Grigoriev and Karpinski (Grigoriev Karpinski 1993) where they provide an elegant algebraic criterion to be satisfied by any t sparse shift for f(x) We use that paper as our starting point for further refinement. The main departure is ....

Borodin, A. and Tiwari, P. (1990), "On the decidability of sparse univariate polynomial interpolation," Proc. 22nd Symp. Theory of Computing, ACM Press, pp. 535--545.

....integers ( 1 ; n ) such that the exponents of f can be recovered from the exponents of all the f(X 1 ; X n ) 2 Complexity issues for t sparse polynomial and rational function interpolation have been dealt with in several papers. Polynomial interpolation was studied in [1] [2], 9] 12] 17] 25] 26] For bounded degree rational interpolation (when the bound on the degree is part of the input) see [15] 16] 23] Approximative unbound interpolation arises also naturally in issues of computational learnability of sparse rational functions (cf. 20] The present ....

Borodin, A. and Tiwari, P.A., On the Decidability of Sparse Univariate Polynomial Interpolation, Research Report RC 14923, IBM T. J. Watson Research Center, New York, 1989.

.... there has been much interest in the design of efficient algorithms for computing sparse representations for various classes of functions such as polynomials, rational functions, and algebraic functions (Grigoriev Karpinski 1987, Clausen et al. 1988, Ben Or Tiwari 1988, Kaltofen Lakshman 1988, Borodin Tiwari 1990, Grigoriev Karpinski Singer 1990,1991,1992, 1993, 1994, Mansour 1992, Lakshman Saunders 1993, 1994) The problem of finding sparsifying invertible linear tranformations for polynomials in F [x 1 ; x 2 ; x n ] was first addressed in a recent paper by Grigoriev and Karpinski ....

Borodin, A. and Tiwari, P. (1990), "On the decidability of sparse univariate polynomial interpolation," Proc. 22nd Symp. Theory of Computing, ACM Press, pp. 535--545.

....( 1 ; n ) such that the exponents of f can be recovered from the exponents of all the f(X 1 ; X n ) Complexity issues for t sparse polynomial and rational function interpolation have been dealt with in several papers. Polynomial (black box) interpolation was studied in [1] [2], 9] 12] 17] 19] 27] 28] For bounded degree rational interpolation (when the bound on the degree is part of the input) see [15] 16] 25] Approximative unbound interpolation arises also naturally in issues of computational learnability of sparse rational functions (cf. 21] The ....

Borodin, A. and Tiwari, P.A., On the Decidability of Sparse Univariate Polynomial Interpolation, Research Report RC 14923, IBM T. J. Watson Research Center, New York, 1989.

....is of great importance in computational algebra. Sparse interpolation has received significant attention in several recent papers (Ben or and Tiwari (1988) Clausen et al. (1988) Kaltofen and Lakshman (1988) Grigoriev and Karpinski (1987) Grigoriev, Karpinski, and Singer (1990, 1991a, 1991b) Borodin and Tiwari (1990), Zippel (1990) In particular, the problem of interpolating a t sparse univariate polynomial given a black box for evaluating the polynomial can be efficiently solved using Ben Or and Tiwari s adaptation of the BCH decoding algorithm. Sparse interpolation is well recognized as a very useful tool ....

.... Gamma 1) correspond to polynomials that are t sparse in the Pochhammer basis. We use the Pochhammer case as a motivating example for our discussion of the Chebyshev case. The problem of efficiently interpolating polynomials that are sparse in the Chebyshev basis was stated as an open problem in Borodin and Tiwari (1990). Our algorithm provides a solution and it is another generalization of the algorithm of Ben Or and Tiwari. It uses properties shared by the standard power basis and the Chebyshev polynomials and appears to be different from the generalizations presented in (Dress and Grabmeier (1991) Grigoriev, ....

Borodin, A. and Tiwari, P. (1990), "On the decidability of sparse univariate polynomial interpolation,"Proc. 22nd Symp. Theory of Computing, ACM Press, pp. 535-- 545.

....returns the value of the function at a. There are a number of classes of arithmetic formulas that can be interpolated sequentially in polynomial time as well as in parallel in polylogarithmic time (with polynomially many processors) These include sparse polynomials and sparse rational functions ([BT88, BT90, GKS90b, GrKS88, RB89, GKS90b, SS93, M91]) A formula over a variable set V is read once if each variable appears at most once in it. An arithmetic read once formula over a field K is a read once formula over the basic operations of the field K; addition, subtraction, multiplication, division, and constants are also permitted in the ....

A. BORODIN AND P. TIWARI, On the decidability of sparse univariate polynomial interpolation, Comput. Complexity, 1 (1991), pp. 67--90.

....no more than t terms) such that f(x) g 1 (g 2 ( g s (x) if they exist. Recently, there has been much interest in the design of efficient algorithms for computing sparse representations for various classes of functions such as polynomials, rational functions, and algebraic functions [1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 14, 18, 21]. Sparse interpolation is well recognized as a very useful tool for controlling intermediate expression swell in computer algebra [15, 24] Sparse polynomials and rational functions can be evaluated quickly and that makes them attractive to several applications and an interesting line of research ....

.... sparse interpolation algorithm that works for a class of bases (which includes the Pochhammer basis) can be found in [10] Computing t sparse shifts and the representation of f(x) in the basis 1; x Gamma ff; x Gamma ff) 2 ; was raised as an open problem by Borodin and Tiwari in [2]. Subsequently, the problem was taken up in a recent paper by Grigoriev and Karpinski [11] where they provide an elegant algebraic criterion to be satisfied by any t sparse shift for f(x) We use the above paper of Grigoriev and Karpinski as our starting point for further refinement. The main ....

Borodin, A. and Tiwari, P. (1990), "On the decidability of sparse univariate polynomial interpolation," Proc. 22nd Symp. Theory of Computing, ACM Press, pp. 535--545.

....the value of the function at a. There are a number of classes of arithmetic formulas that can be interpolated sequentially in polynomial time as well as in parallel in poly logarithmic time (with polynomially many processors) These include sparse polynomials and sparse rational functions ([BT88,BT90,GKS90,GrKS88,RB89,M91]) Research supported in part by NSERC of Canada. Author s E mail addresses: bshouty cpsc.ucalgary.ca and cleve cpsc.ucalgary.ca. A formula over a variable set V is read once if each variable appears at most once in it. An arithmetic read once formula over a field K is a read once formula ....

A. Borodin and P. Tiwari. On the Decidability of Sparse Univariate Polynomial Interpolation. Computational Complexity, 1, 1991.

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A. BORODIN AND P. TIWARI, On the decidability of sparse univariate polynomial interpolation, Comput. Complexity, 1 (1991), pp. 67--90.

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A. Borodin and P. Tiwari. On the Decidability of Sparse Univariate Polynomial Interpolation. Computational Complexity, 1, 1991.

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A. Borodin and P. Tiwari. On the Decidability of Sparse Univariate Polynomial Interpolation, Proc. 22nd Ann. ACM Symp. on Theory of Computing, 535--545, ACM Press, New York, 1990.

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A. Borodin and P. Towari, "On the decidability of sparse univariate polynomial interpolation ", Computational Complexity, vol.1, 1991, pp.67-90

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A. Borodin and P. Tiwari, On the Decidability of Sparse Univariate Polynomial Interpolation, Proc. 22nd ACM STOC (1990), pp. 535-- 545.

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Borodin, A., Tiwari, P., On the Decidability of Sparse Univariate Polynomial Interpolation, IBM Research Report RC 14923 (#66763), Sep. 1989.

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A. Borodin, P. Tiwari, On the Decidability of Sparse Univariate Polynomial Interpolation, Proc. 22nd ACM STOC (1990), pp. 535--545.

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A. Borodin, P. Tiwari, On the Decidability of Sparse Univariate Polynomial Interpolation, Proc. 22nd ACM STOC (1990), pp. 535--545.

No context found.

A. Borodin, P. Tiwari, On the Decidability of Sparse Univariate Polynomial Interpolation, Proc. 22nd ACM STOC (1990), pp. 535--545.

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A. Borodin, P. Tiwari, On the Decidability of Sparse Univariate Polynomial Interpolation, Proc. 22nd ACM STOC (1990), pp. 535--545.

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