The usual 'implementation' of real numbers as floating point numbers on existing computers has the well-known disadvantage that most of the real numbers are not exactly representable in floating point. Also the four basic arithmetic operations can usually not be performed exactly. During the last years research in different areas has been ...
This collection of papers on scientific computing with validation covers the design of floating point units, algorithms for floating point operations, and elementary function evaluations with maximum accuracy. Scientific computing methods are discussed for areas of applied mathematics such as numerical linear algebra, nonlinear equations, global ...
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