%0 Journal Article %1 Clauss2009-xm %A Clauss, P %A Fernandez, F J %A Garbervetsky, D %A Verdoolaege, S %D 2009 %J IEEE Trans. Very Large Scale Integr. VLSI Syst. %K Bernstein_expansion Memory_usage_estimation Polyhedral_model To_Read convex_polytopes convex_sets embedded_systems finite_element_analysis memory_requirement memory_requirement_estimation polynomial_approximation program_optimization static_program_analysis symbolic_polynomial_maximization %N 8 %P 983--996 %T Symbolic Polynomial Maximization Over Convex Sets and Its Application to Memory Requirement Estimation %V 17 %X Memory requirement estimation is an important issue in the development of embedded systems, since memory directly influences performance, cost and power consumption. It is therefore crucial to have tools that automatically compute accurate estimates of the memory requirements of programs to better control the development process and avoid some catastrophic execution exceptions. Many important memory issues can be expressed as the problem of maximizing a parametric polynomial defined over a parametric convex domain. Bernstein expansion is a technique that has been used to compute upper bounds on polynomials defined over intervals and parametric ldquoboxesrdquo. In this paper, we propose an extension of this theory to more general parametric convex domains and illustrate its applicability to the resolution of memory issues with several application examples.

@article{Clauss2009-xm, abstract = {Memory requirement estimation is an important issue in the development of embedded systems, since memory directly influences performance, cost and power consumption. It is therefore crucial to have tools that automatically compute accurate estimates of the memory requirements of programs to better control the development process and avoid some catastrophic execution exceptions. Many important memory issues can be expressed as the problem of maximizing a parametric polynomial defined over a parametric convex domain. Bernstein expansion is a technique that has been used to compute upper bounds on polynomials defined over intervals and parametric ldquoboxesrdquo. In this paper, we propose an extension of this theory to more general parametric convex domains and illustrate its applicability to the resolution of memory issues with several application examples.}, added-at = {2015-04-11T18:41:09.000+0200}, author = {Clauss, P and Fernandez, F J and Garbervetsky, D and Verdoolaege, S}, biburl = {https://www.bibsonomy.org/bibtex/278d0781cf671023cddae9b62179f6d62/christophv}, interhash = {0f80c25a467c90924ed5e951ada0e3d2}, intrahash = {78d0781cf671023cddae9b62179f6d62}, journal = {IEEE Trans. Very Large Scale Integr. VLSI Syst.}, keywords = {Bernstein_expansion Memory_usage_estimation Polyhedral_model To_Read convex_polytopes convex_sets embedded_systems finite_element_analysis memory_requirement memory_requirement_estimation polynomial_approximation program_optimization static_program_analysis symbolic_polynomial_maximization}, month = aug, number = 8, pages = {983--996}, timestamp = {2015-04-11T18:41:09.000+0200}, title = {Symbolic Polynomial Maximization Over Convex Sets and Its Application to Memory Requirement Estimation}, volume = 17, year = 2009 }