The Vector QD Algorithm for Smooth Functions (f, f′)

Computing f(A)b for Matrix Functions f

For matrix functions f we investigate how to compute a matrix-vector product f (A)b without explicitly computing f (A). A general method is described that applies quadrature to the matrix version of the Cauchy integral theorem. Methods specific to the logarithm, based on quadrature, and fractional matrix powers, based on solution of an ordinary differential equation initial value problem, are a...

The Definition of the Functions f , F and F in the

It is demonstrated that the system of coordinates {M, t} defined by Ruban and Chernin is unique, where two undetermined functions of the Tolman-Bondi (TB) model, f(M) and F (M), are dependent. Two initial conditions of the model are calculated through an initial profiles of density and energy, both are given as function of coordinate M . It is shown that in a general case of an arbitrary co-mov...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

F . 1 Why Vector Processors ?

The f-Vector of the Descent Polytope

For a positive integer n and a subset S ⊆ [n−1], the descent polytope DPS is the set of points (x1, . . . , xn) in the n-dimensional unit cube [0,1]n such that xi ≥ xi+1 if i ∈ S and xi ≤ xi+1 otherwise. First, we express the f -vector as a sum over all subsets of [n− 1]. Second, we use certain factorizations of the associated word over a two-letter alphabet to describe the f -vector. We show t...