Yasuhiko Ikebe. The Galerkin method for the numerical solution of Fredholm integral equations of the second kind. SIAM Review, 14(3):465--491, July 1972. Home/Search Document Not in Database Summary Related Articles Check |
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in Global Illumination * - James Arvo Program (Correct)
.... Figure (2) To see the Galerkin method another way, let P, be the projection operator onto X, Then solving equation (59) is equivalent to finding f X, such that P, L g) O, which is equivalent to solving (I P, K)f, since have had their ranges collapsed onto the n dimensional space X, [17]. equation (55) equation (59) is equivalent to So the Galerkin method seeks a solution that is exact once K and g In analogy with for i: 1, n. Equivalently, 60) which is analogous to equation (56) Following the very same steps as in the least squares method, we arrive at the expression ....
Yasuhiko Ikebe. The Galerkin method for the numerical solution of Fredholm integral equations of the second kind. SIAM Review, 14(3):465 491, July 1972.
Linear Operators and Integral Equations in Global Illumination - Arvo (1993) (1 citation) (Correct)
....(59) is equivalent to finding f n 2 X n such that P n ( b f n Gamma g) 0; which is equivalent to solving (I Gamma P n K)f n = P n g; since P n f n = f n . So the Galerkin method seeks a solution that is exact once K and g have had their ranges collapsed onto the n dimensional space X n [17]. In analogy with equation (55) equation (59) is equivalent to D b f n Gamma g fi fi fi u i E = 0 (60) for i = 1; n. Equivalently, hg j u i i = D b f n fi fi fi u i E which is analogous to equation (56) Following the very same steps as in the least squares method, we arrive at ....
Yasuhiko Ikebe. The Galerkin method for the numerical solution of Fredholm integral equations of the second kind. SIAM Review, 14(3):465--491, July 1972.
Linear Operators and Transfer Equations in Global Illumination - Arvo (Correct)
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Yasuhiko Ikebe. The Galerkin method for the numerical solution of Fredholm integral equations of the second kind. SIAM Review, 14(3):465--491, July 1972.
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