| Matrix decomposition algorithms employing fast Fourier transforms were developed recently by the authors to solve the systems of linear algebraic equations that arise when piecewise Hermite bicubic orthogonal spline collocation (OSC) is applied to certain separable elliptic boundary value problems on a rectangle. In this paper, these algorithms are interpreted as Fourier methods in analogy wi...

In semide nite programming one minimizes a linear function subject to the constraint that an a ne combination of symmetric matrices is positive semide nite. Such a constraint is nonlinear and nonsmooth, but convex, so semide nite programs are convex optimization problems. Semide nite programming uni es several standard problems (e.g., linear and quadratic programming) and nds many applications ...

Michael G. Oliva, Ph.D. Professor Department of Civil and Environmental Engineering University of Wisconsin–Madison Madison, Wisconsin The in-plane fl exibility of untopped precast concrete double-tee diaphragms is often ignored in current design practice. The performance of parking structures during earthquakes and subsequent research studies have shown, however, that in-plane fl exibility of ...

The main object of this paper is to give a di erent approach to proof of generating matrix functions for Laguerre matrix polynomials. We also obtain the hypergeometric matrix representations, addition theorem, nite summation formula and an integral representation for Laguerre matrix polynomials. We get the relations between Laguerre, Legendre and Hermite matrix polynomials. We get the generatin...

Various classes of nite-dimensional closed convex cones are studied. Equivalent characterizations of pointed cones, pyramids and rational pyramids are given. Special class of regular cones, corresponding to \continuous linear" quasiorderings of integer vectors is introduced and equivalently characterized. It comprehends both pointed cones and rational pyramids. Two diierent ways of determining ...

The Conjugate Gradient (CG) method is an iterative algorithm for solving linear systems of equations Ax = b, where A is symmetric and positive de nite. The convergence of the method depends on the spectrum of A; when its eigenvalues are clustered, the method converges rapidly. In particular, CG converges to within a xed tolerance in O( √ κ), where κ = κ(A) = λmax(A)/λmin(A) is the spectral cond...

Decentralized finance (DeFi) has exploded in popularity with a billion-dollar market cap. While uncollateralized lending, known as flash loan, emerged from DeFi, it become primary tool used by attackers to drain investment tokens DeFi networks. The existing countermeasures seem practical, but no comprehensive quantitative analysis framework was available test them. This paper proposes the Flash...