We propose a method for support vector machine classification using indefinite kernels. Instead of directly minimizing or stabilizing a nonconvex loss function, our algorithm simultaneously computes support vectors and a proxy kernel matrix used in forming the loss. This can be interpreted as a penalized kernel learning problem where indefinite kernel matrices are treated as a noisy observation...

This note is a detailed explanation of Shanks–Atkin NUCOMP— composition and reduction carried out “simultaneously”—for all quadratic fields, that is, including real quadratic fields. That explanation incidentally deals with various “exercises” left for confirmation by the reader in standard texts. Extensive testing in both the numerical and function field cases by Michael J Jacobson, Jr, report...

In this paper, we consider the indefinite scalar curvature problem on R. We propose new conditions on the prescribing scalar curvature function such that the scalar curvature problem on R (similarly, on S ) has at least one solution. The key observation in our proof is that we use the bifurcation method to get a large solution and then after establishing the Harnack inequality for solutions nea...

We consider the problem of convergence and error estimation of the method for computing indefinite integrals proposed in [P. Keller, A method for indefinite integration of oscillatory and singular functions, Numerical Algorithms 46(3) (2007), 219–251]. To this end, we have analysed the properties of the difference operator related to the difference equation for the Chebyshev coefficients of a f...