COMPUTING Aα, log( A ), AND RELATED MATRIX FUNCTIONS BY CONTOUR INTEGRALS
New methods are proposed for the numerical evaluation of f(A) or f(A)b, where f(A) is a function such as A 1/2 or log(A) with singularities in (—∞, 0] and A is a matrix with eigenvalues on or near (0, ∞). The methods are based on combining contour integrals evaluated by the periodic trapezoid rule w...
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| Veröffentlicht in: | SIAM journal on numerical analysis 2008-01, Vol.46 (5), p.2505-2523 |
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| container_title | SIAM journal on numerical analysis |
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| creator | HALE, NICHOLAS HIGHAM, NICHOLAS J. TREFETHEN, LLOYD N. |
| description | New methods are proposed for the numerical evaluation of f(A) or f(A)b, where f(A) is a function such as A 1/2 or log(A) with singularities in (—∞, 0] and A is a matrix with eigenvalues on or near (0, ∞). The methods are based on combining contour integrals evaluated by the periodic trapezoid rule with conformal maps involving Jacobi elliptic functions. The convergence is geometric, so that the computation of f(A)b is typically reduced to one or two dozen linear system solves, which can be carried out in parallel. |
| doi_str_mv | 10.1137/070700607 |
| format | Article |
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| ispartof | SIAM journal on numerical analysis, 2008-01, Vol.46 (5), p.2505-2523 |
| issn | 0036-1429 1095-7170 |
| language | eng |
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| source | SIAM Journals Online; JSTOR Mathematics & Statistics; Jstor Complete Legacy |
| subjects | Approximation Eigenvalues Elliptic functions Integrals Mathematical functions Mathematical integrals Matrices Methods Perceptron convergence procedure Rectangles Trapezoidal rule |
| title | COMPUTING Aα, log( A ), AND RELATED MATRIX FUNCTIONS BY CONTOUR INTEGRALS |
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