partial pivoting
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1: 3.2 Linear Algebra
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βΊTo avoid instability the rows are interchanged at each elimination step in such a way that the absolute value of the element that is used as a divisor, the pivot element, is not less than that of the other available elements in its column.
…This modification is called Gaussian elimination with partial pivoting.
βΊFor more information on pivoting see Golub and Van Loan (1996, pp. 109–123).
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βΊAssume that can be factored as in (3.2.5), but without partial pivoting.
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2: 1.5 Calculus of Two or More Variables
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§1.5(i) Partial Derivatives
… βΊThe function is continuously differentiable if , , and are continuous, and twice-continuously differentiable if also , , , and are continuous. … βΊSufficient conditions for validity are: (a) and are continuous on a rectangle , ; (b) when both and are continuously differentiable and lie in . … βΊSuppose that are finite, is finite or , and , are continuous on the partly-closed rectangle or infinite strip . Suppose also that converges and converges uniformly on , that is, given any positive number , however small, we can find a number that is independent of and is such that …3: 19.18 Derivatives and Differential Equations
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βΊLet , and be an -tuple with 1 in the th place and 0’s elsewhere.
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βΊIf , then elimination of between (19.18.11) and (19.18.12), followed by the substitution , produces the Gauss hypergeometric equation (15.10.1).
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19.18.14
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19.18.15
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19.18.16
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4: 36.10 Differential Equations
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§36.10(ii) Partial Derivatives with Respect to the
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36.10.7
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36.10.8
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36.10.10
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§36.10(iv) Partial -Derivatives
…5: 16.14 Partial Differential Equations
§16.14 Partial Differential Equations
βΊ§16.14(i) Appell Functions
βΊ6: 10.38 Derivatives with Respect to Order
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10.38.2
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βΊFor at combine (10.38.1), (10.38.2), and (10.38.4).
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10.38.4
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10.38.7
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