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Several problems in the implementations of control systems, signal-processing systems, and scientific computing systems reduce to compiling a polynomial expression over the reals into an imperative program using fixed-point arithmetic. Fixed-point arithmet ...
Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued implementation and sp ...
Several problems in the implementations of control systems, signal-processing systems, and scientific computing systems reduce to compiling a polynomial expression over the reals into an imperative program using fixed-point arithmetic. Fixed-point arithmet ...
A large portion of software is used for numerical computation in mathematics, physics and engineering. Among the aspects that make verification in this domain difficult is the need to quantify numerical errors, such as roundoff errors and errors due to the ...
We formulate and derive a generalization of an orthogonal rational-function basis for spectral expansions over the infinite or semi-infinite interval. The original functions, first presented by Wiener, are a mapping and weighting of the Fourier basis to th ...
This work focuses on the finite element discretization of boundary value problems whose solution features either a discontinuity or a discontinuous conormal derivative across an interface inside the computational domain. The interface is characterized via ...
A large portion of software is used for numerical calculations in mathematics, physics and engineering applications. Among the things that make verification in this domain difficult is the quantification of numerical errors, such as roundoff errors and err ...
We analyze the efficiency of available algorithms for the simulation of classical fidelity and show that their computational costs increase exponentially with the number of degrees of freedom. Then we present an algorithm for which the number of trajectori ...
Synthesis of programs or their fragments is a way to write programs by providing only their meaning without worrying about the implementation details. It avoids the drawback of writing sequential code, which might be difficult to check, error-prone or tedi ...
A new method for measuring shape rectangularity is introduced. The new shape measure is invariant with respect to similarity transformations, ranges over the interval (0,1] and picks the value 1 if and only if the measured shape is a rectangle. The measure ...
