Fast Monte-Carlo Algorithms for finding Low
... is the problem of finding a low-rank approximation, i.e., given an m × n matrix A, find a matrix D of rank at most k so that ||A − D||F is asPsmall as possible. (For any matrix M, the Frobenius norm, ||.||F , is defined as ||M||2F = i,j Mij2 ). Alternatively, if we view the rows of A as points in Rn ...
... is the problem of finding a low-rank approximation, i.e., given an m × n matrix A, find a matrix D of rank at most k so that ||A − D||F is asPsmall as possible. (For any matrix M, the Frobenius norm, ||.||F , is defined as ||M||2F = i,j Mij2 ). Alternatively, if we view the rows of A as points in Rn ...
4.2 Every PID is a UFD
... I1 ⊆ I 2 ⊆ I 3 ⊆ . . . is a chain of ideals in R, then there is some m for which Ik = Im for all k ≥ m. Note: Commutative rings satisfying the ACC are called Noetherian. To understand what the ACC means it may be helpful to look at an example of a ring in which it does not hold. Example 4.2.2 Let C( ...
... I1 ⊆ I 2 ⊆ I 3 ⊆ . . . is a chain of ideals in R, then there is some m for which Ik = Im for all k ≥ m. Note: Commutative rings satisfying the ACC are called Noetherian. To understand what the ACC means it may be helpful to look at an example of a ring in which it does not hold. Example 4.2.2 Let C( ...
GUIDELINES FOR AUTHORS
... We fix the function of these two arguments g , T F l , , t as the result of action of functional T , under the stipulation that, values of variable and are constant. As a result of functional T we have matrix, the elements of matrix are values t ij T F l j , i , t ...
... We fix the function of these two arguments g , T F l , , t as the result of action of functional T , under the stipulation that, values of variable and are constant. As a result of functional T we have matrix, the elements of matrix are values t ij T F l j , i , t ...