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Interval package: Difference between revisions
Improved accuracy of linear system solving operations
m (Updated accuracy of matrix operations) |
(Improved accuracy of linear system solving operations) |
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''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 for vector and matrix operations.'' | ''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 for vector and matrix operations.'' | ||
octave:1> A = infsup ([1, 2, 3; 4, 0, 0; 0, 0, | octave:1> A = infsup ([1, 2, 3; 4, 0, 0; 0, 0, 1], [1, 2, 3; 4, 0, 6; 0, 0, 1]) | ||
A = 3×3 interval matrix | A = 3×3 interval matrix | ||
[1] [2] [3] | [1] [2] [3] | ||
[4] [0] [0, 6] | [4] [0] [0, 6] | ||
[0] [0] | [0] [0] [1] | ||
octave:2> B = inv (A) | octave:2> B = inv (A) | ||
B = 3×3 interval matrix | B = 3×3 interval matrix | ||
[0] [.25] [ | [0] [.25] [-1.5, 0] | ||
[.5] [-.125] | [.5] [-.125] [-1.125] | ||
[0] [0] | [0] [0] [1] | ||
octave:3> A * B | octave:3> A * B | ||
ans = 3×3 interval matrix | ans = 3×3 interval matrix | ||
[1] [0] [ | [1] [0] [-.75, +.75] | ||
[0] [1] | [0] [1] [-6, +6] | ||
[0] [0] | [0] [0] [1] | ||
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c ⊂ 3×1 interval vector | c ⊂ 3×1 interval vector | ||
[. | [.18333333333333332, .18333333333333341] | ||
[. | [.43333333333333323, .43333333333333352] | ||
[.18333333333333326, .1833333333333333] | |||
octave:6> A * c | octave:6> A * c | ||
ans ⊂ 3×1 interval vector | ans ⊂ 3×1 interval vector | ||
[2. | [2.9999999999999991, 3.0000000000000009] | ||
[3. | [3.9999999999999986, 4.0000000000000009] | ||
[4. | [4.9999999999999982, 5.0000000000000027] | ||
=== Error handling === | === Error handling === | ||