Slides
... Don‘t know of k x n matrices S with small k for which if x‘ is solution to minx |(SA)x-(Sb)|1 then |Ax‘-b|1 · (1+ε) minx |Ax-b|1 with high probability Instead: can find an S so that |Ax‘-b|1 · (d log d) minx |Ax-b|1 S is a matrix of i.i.d. Cauchy random variables ...
... Don‘t know of k x n matrices S with small k for which if x‘ is solution to minx |(SA)x-(Sb)|1 then |Ax‘-b|1 · (1+ε) minx |Ax-b|1 with high probability Instead: can find an S so that |Ax‘-b|1 · (d log d) minx |Ax-b|1 S is a matrix of i.i.d. Cauchy random variables ...
M04/01
... More sophisticated tools have largely replaced multiplication tables of groups. However when associativity is dropped many of these tools are no longer available and often examples are constructed by indicating a multiplication table. A generalization of Ward quasigroups is obtained when the operati ...
... More sophisticated tools have largely replaced multiplication tables of groups. However when associativity is dropped many of these tools are no longer available and often examples are constructed by indicating a multiplication table. A generalization of Ward quasigroups is obtained when the operati ...
Fast sparse matrix multiplication ∗
... for finding simple cycles in graphs [AYZ95, AYZ97, YZ04], for finding small cliques and other small subgraphs [NP85], for finding shortest paths [Sei95, SZ99, Zwi02], for obtaining improved dynamic reachability algorithms [DI00, RZ02], and for matching problems [MVV87, RV89, Che97]. Other applicatio ...
... for finding simple cycles in graphs [AYZ95, AYZ97, YZ04], for finding small cliques and other small subgraphs [NP85], for finding shortest paths [Sei95, SZ99, Zwi02], for obtaining improved dynamic reachability algorithms [DI00, RZ02], and for matching problems [MVV87, RV89, Che97]. Other applicatio ...
The quadprog Package
... matrix containing the non-zero elements of the matrix A that defines the constraints. If mi denotes the number of non-zero elements in the i-th column of A then the first mi entries of the i-th column of Amat hold these non-zero elements. (If maxmi denotes the maximum of all mi , then each column of ...
... matrix containing the non-zero elements of the matrix A that defines the constraints. If mi denotes the number of non-zero elements in the i-th column of A then the first mi entries of the i-th column of Amat hold these non-zero elements. (If maxmi denotes the maximum of all mi , then each column of ...
Sketching as a Tool for Numerical Linear Algebra (slides)
... 2. Project each of the rows onto S*A 3. Find best rank-k approximation of projected points inside of rowspace of S*A (easy) Bottleneck is step 2 [CW] Turns out you can approximate the projection Sketching for generalized regression again: minX |X(SA)-A|F2 ...
... 2. Project each of the rows onto S*A 3. Find best rank-k approximation of projected points inside of rowspace of S*A (easy) Bottleneck is step 2 [CW] Turns out you can approximate the projection Sketching for generalized regression again: minX |X(SA)-A|F2 ...
