Interval package: Difference between revisions

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Above mentioned operations can also be applied element-wise to interval vectors and matrices. Many operations use [http://www.gnu.org/software/octave/doc/interpreter/Vectorization-and-Faster-Code-Execution.html#Vectorization-and-Faster-Code-Execution vectorization techniques].
Above mentioned operations can also be applied element-wise to interval vectors and matrices. Many operations use [http://www.gnu.org/software/octave/doc/interpreter/Vectorization-and-Faster-Code-Execution.html#Vectorization-and-Faster-Code-Execution vectorization techniques].


In addition, there are matrix operations on interval matrices. These operations comprise: exact dot product, exact matrix multiplication, exact vector sums, (not-exact) matrix inversion, matrix powers, and solving linear systems. As a result of missing hardware / low-level library support and missing optimizations, these operations are quite slow compared to familiar operations in floating-point arithmetic. (A [http://books.google.de/books?hl=de&id=I7X9EVfeV5EC&q=accumulator Kulisch accumulator] in hardware could improve the computation speed of the exact operations a lot.)
In addition, there are matrix operations on interval matrices. These operations comprise: exact dot product, exact matrix multiplication, exact vector sums, (not-exact) matrix inversion, matrix powers, and solving linear systems. As a result of missing hardware / low-level library support and missing optimizations, these operations are quite slow compared to familiar operations in floating-point arithmetic.
 
''Technical background information: The interval package simulates a [http://books.google.de/books?hl=de&id=I7X9EVfeV5EC&q=accumulator Kulisch accumulator] in software to produce tightly rounded results.''
  octave:1> A = infsup ([1, 2, 3; 4, 0, 0; 0, 0, 0], [1, 2, 3; 4, 0, 6; 0, 0, 1])
  octave:1> A = infsup ([1, 2, 3; 4, 0, 0; 0, 0, 0], [1, 2, 3; 4, 0, 6; 0, 0, 1])
  A = 3×3 interval matrix
  A = 3×3 interval matrix
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