A Modified Affine Arithmetic Method for Computational Error Analysis
نویسندگان
چکیده
منابع مشابه
Floating-point error analysis based on affine arithmetic
During the development of floating-point signal processing systems, an efficient error analysis method is needed to guarantee the output quality. We present a novel approach to floating-point error bound analysis based on affine arithmetic. The proposed method not only provides a tighter bound than the conventional approach, but also is applicable to any arithmetic operation. The error estimati...
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...
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...
متن کاملEfficient Algorithms and Error Analysis for the Modified Nystrom Method
Lemma 8. Given an m × m symmetric matrix A and a target rank k, we let C1 contain the c1 columns of A selected by a column sampling algorithm such that the following inequality holds: ∥∥A− PC1A∥∥2F ≤ f∥∥A−Ak∥∥2F . Then we select c2 = kf −1 columns to construct C2 and c3 = (c1+ c2) −1 columns to construct C3, both using the adaptive sampling according to the residual B1 = A − PC1A and B2 = A − P...
متن کاملAffine Arithmetic
We give a formalization of affine forms [1, 2] as abstract representations of zonotopes. We provide affine operations as well as overapproximations of some non-affine operations like multiplication and division. Expressions involving those operations can automatically be turned into (executable) functions approximating the original expression in affine arithmetic. Moreover we give a verified im...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: DEStech Transactions on Engineering and Technology Research
سال: 2017
ISSN: 2475-885X
DOI: 10.12783/dtetr/imeia2016/9230