Xiao Dong Shi and Hong Liu, The integral expression and numerical
... Where un is the outward scattering coefficient, H (kr ) is the first kind n-order Hankel function, the subscript ‘>’ means ‘outward’, is the outward angle between the normal and the outgoing wave, k is the wavenumber, ...
... Where un is the outward scattering coefficient, H (kr ) is the first kind n-order Hankel function, the subscript ‘>’ means ‘outward’, is the outward angle between the normal and the outgoing wave, k is the wavenumber, ...
QR-method lecture 2 - SF2524 - Matrix Computations for Large
... Complexity of one QR-step for a Hessenberg matrix We need to apply 2(m − 1) givens rotators to compute one QR-step. One givens rotator applied to a vector can be computed in O(1) operations. One givens rotator applied to matrix can be computed in O(m) operations. ...
... Complexity of one QR-step for a Hessenberg matrix We need to apply 2(m − 1) givens rotators to compute one QR-step. One givens rotator applied to a vector can be computed in O(1) operations. One givens rotator applied to matrix can be computed in O(m) operations. ...
Almost Block Diagonal Linear Systems
... For the mesh π of (2..3), let Mr (π) = {v ∈ C 1 [a, b] : v|[xi−1 ,xi ] ∈ Pr , i = 1, 2, . . . , N }, where Pr denotes the set of all polynomials of degree ≤ r. Also, let M0r (π) = Mr (π) ∩ {v|v(a) = v(b) = 0}. ...
... For the mesh π of (2..3), let Mr (π) = {v ∈ C 1 [a, b] : v|[xi−1 ,xi ] ∈ Pr , i = 1, 2, . . . , N }, where Pr denotes the set of all polynomials of degree ≤ r. Also, let M0r (π) = Mr (π) ∩ {v|v(a) = v(b) = 0}. ...
