@misc{SchaedleLopezFernandezLubich2005, author = {Sch{\"a}dle, Achim and Lopez-Fernandez, Maria and Lubich, Christian}, title = {Fast and oblivious convolution quadrature}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8437}, number = {05-09}, year = {2005}, abstract = {We give an algorithm to compute \$N\$ steps of a convolution quadrature approximation to a continuous temporal convolution using only \$O(N\, \log N)\$ multiplications and \$O(\log N)\$ active memory. The method does not require evaluations of the convolution kernel, but instead \$O(\log N)\$ evaluations of its Laplace transform, which is assumed sectorial. The algorithm can be used for the stable numerical solution with quasi-optimal complexity of linear and nonlinear integral and integro-differential equations of convolution type. In a numerical example we apply it to solve a subdiffusion equation with transparent boundary conditions.}, language = {en} }