Jiawei Chiu

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When a matrix A with n columns is known to be well-approximated by a linear combination of basis matrices B1, . . . , Bp, we can apply A to a random vector and solve a linear system to recover this linear combination. The same technique can be used to obtain an approximation to A−1. A basic question is whether this linear system is well-conditioned. This is(More)
This paper considers the problem of approximating the inverse of the wave-equation Hessian, also called normal operator, in seismology and other types of wave-based imaging. An expansion scheme for the pseudodifferential symbol of the inverse Hessian is set up. The coefficients in this expansion are found via least-squares fitting from a certain number of(More)
A skeleton decomposition of a matrix A is any factorization of the form A:CZAR:, where A:C comprises columns of A, and AR: comprises rows of A. In this paper, we investigate the conditions under which random sampling of C and R results in accurate skeleton decompositions. When the singular vectors (or more generally the generating vectors) are incoherent,(More)
Nonlinear Laplacian spectral analysis (NLSA) is a method for spatiotemporal analysis of high-dimensional data, which represents temporal patterns via orthonormal basis functions on the nonlinear data manifold. Through the use of such basis functions (determined by means of graph Laplace-Beltrami eigenfunction algorithms), NLSA captures intermittency, rare(More)
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