Modified affine arithmetic in tensor form for trivariate polynomial evaluation and algebraic surface plotting
نویسندگان
چکیده
منابع مشابه
Modified Affine Arithmetic in Tensor Form for Trivariate Polynomial Evaluation and Algebraic Surface Plotting ⋆
This paper extends the modified affine arithmetic in matrix form method for bivariate polynomial evaluation and algebraic curve plotting in 2D to modified affine arithmetic in tensor form for trivariate polynomial evaluation and algebraic surface plotting in 3D. Experimental comparison shows that modified affine arithmetic in tensor form is not only more accurate but also much faster than stand...
متن کاملModified Affine Arithmetic in Tensor Form ⋆
This paper extends the modified affine arithmetic in matrix form method for bivariate polynomial evaluation and algebraic curve plotting in 2D to modified affine arithmetic in tensor form for trivariate polynomial evaluation and algebraic surface plotting in 3D. Experimental comparison shows that modified affine arithmetic in tensor form is not only more accurate but also much faster than affin...
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We compare approaches to location of the algebraic curve f(x, y) = 0 in a rectangular region of the plane, based on recursive use of conservative estimates of the range of the function over a rectangle. Previous work showed that performing interval arithmetic in the Bernstein basis is more accurate than using the power basis, and that affine arithmetic in the power basis is better than using in...
متن کاملModified Affine Arithmetic Is More Accurate than Centered Interval Arithmetic or Affine Arithmetic
In this paper we give mathematical proofs of two new results relevant to evaluating algebraic functions over a box-shaped region: (i) using interval arithmetic in centered form is always more accurate than standard affine arithmetic, and (ii) modified affine arithmetic is always more accurate than interval arithmetic in centered form. Test results show that modified affine arithmetic is not onl...
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The title of my lecture is, I am afraid, probably misleading and certainly too ambitious. For, on the one hand, the connection between arithmetic and geometry suggested by it is not the modern development in divisors theory, but an application of algebraic geometry for arithmetical purposes. On the other hand, I shall confine the subject of this lecture to cubic surfaces in ordinary space, cons...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2006
ISSN: 0377-0427
DOI: 10.1016/j.cam.2005.08.003