in this paper, the accuracy of k- and k- turbulence models in super sonic boundary layer capturing of smooth/rough flat plates have been comprehensively investigated. among these investigations, some sorts of sensitivity analysis, including change in turbulence model, generated-grid density, near wall affects, c magnitude (for boundary layers generated on smooth flat plates), and change in c...

• Many kernel-based learning algorithms have the computational load. • The Nyström low-rank approximation is designed for reducing the computation. • We propose the spectrum decomposition condition with a theoretical justification. • Asymptotic error bounds on eigenvalues and eigenvectors are derived. • Numerical experiments are provided for covariance kernel and Wishart matrix. AMS subject cla...

We present a family of algorithms for computing symmetric rank-revealing VSV decompositions, based on triangular factorization of the matrix. The VSV decomposition consists of a middle symmetric matrix that reveals the numerical rank in having three blocks with small norm, plus an orthogonalmatrix whose columns span approximations to the numerical range and null space. We show that for semi-de ...

We consider the problem of learning multi-ridge functions of the form f(x) = g(Ax) from point evaluations of f . We assume that the function f is defined on an `2-ball in R, g is twice continuously differentiable almost everywhere, and A ∈ Rk×d is a rank k matrix, where k d. We propose a randomized, polynomial-complexity sampling scheme for estimating such functions. Our theoretical development...

We present the first range result for the total K-theory of C∗-algebras. This invariant has been used successfully to classify certain separable, nuclear C∗-algebras of real rank zero. Our results complete the classification of the so-called AD algebras of real rank zero.

we give further results for perron-frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. we indicate two techniques for establishing the main theorem ofperron and frobenius on the numerical range. in the rst method, we use acorresponding version of wielandt's lemma. the second technique involves graphtheory.