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Interval package: Difference between revisions
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# If in addition, each library operation in ''f'' is everywhere continuous on its inputs, while evaluating '''''y''''', then ''f'' is everywhere continuous on '''''x'''''. | # If in addition, each library operation in ''f'' is everywhere continuous on its inputs, while evaluating '''''y''''', then ''f'' is everywhere continuous on '''''x'''''. | ||
# If some library operation in ''f'' is nowhere defined on its inputs, while evaluating '''''y''''', then ''f'' is nowhere defined on '''''x''''', that is Dom(''f'') ∩ '''''x''''' = Ø. | # If some library operation in ''f'' is nowhere defined on its inputs, while evaluating '''''y''''', then ''f'' is nowhere defined on '''''x''''', that is Dom(''f'') ∩ '''''x''''' = Ø. | ||
== What to expect == | |||
The interval arithmetic provided by this interval package is '''slow''' and several functions compute valid enclosures of exact results, but are '''not accurate'''. | |||
''Why is the interval package slow?'' | |||
All arithmetic interval operations are simulated in high-level octave language using floating-point routines, which is a lot slower than hardware implementations [https://books.google.de/books?id=JTc4XdXFnQIC&pg=PA61]. For example, for some tightly rounded results of vector and matrix operations the interval package has to simulate a [http://books.google.de/books?hl=de&id=I7X9EVfeV5EC&q=accumulator Kulisch accumulator], which introduces a computational overhead of factor 10. However, the Kulisch accumulator could be implemented in hardware and then outperform floating-point operations. | |||
== Quick start introduction == | == Quick start introduction == | ||