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SIAMMAX
2010
224views more  SIAMMAX 2010»
13 years 6 months ago
Robust Approximate Cholesky Factorization of Rank-Structured Symmetric Positive Definite Matrices
Abstract. Given a symmetric positive definite matrix A, we compute a structured approximate Cholesky factorization A RT R up to any desired accuracy, where R is an upper triangula...
Jianlin Xia, Ming Gu
SIAMMAX
2010
110views more  SIAMMAX 2010»
13 years 6 months ago
Direction-Preserving and Schur-Monotonic Semiseparable Approximations of Symmetric Positive Definite Matrices
For a given symmetric positive definite matrix A RN
Ming Gu, Xiaoye S. Li, Panayot S. Vassilevski
ADCM
2004
59views more  ADCM 2004»
13 years 11 months ago
Strictly Positive Definite Functions on a Real Inner Product Space
If f(t) = k=0 aktk converges for all t IR with all coefficients ak 0, then the function f(< x, y >) is positive definite on H
Allan Pinkus
MP
2008
82views more  MP 2008»
13 years 11 months ago
Newton's iterates can converge to non-stationary points
Abstract In this note we discuss the convergence of Newton's method for minimization. We present examples in which the Newton iterates satisfy the Wolfe conditions and the Hes...
Walter F. Mascarenhas
FOCS
2008
IEEE
13 years 11 months ago
Matrix Sparsification for Rank and Determinant Computations via Nested Dissection
The nested dissection method developed by Lipton, Rose, and Tarjan is a seminal method for quickly performing Gaussian elimination of symmetric real positive definite matrices who...
Raphael Yuster
ECCV
2010
Springer
13 years 11 months ago
Tensor Sparse Coding for Region Covariances
Sparse representation of signals has been the focus of much research in the recent years. A vast majority of existing algorithms deal with vectors, and higher
Ravishankar Sivalingam, Daniel Boley, Vassilios Mo...
NIPS
2004
14 years 26 days ago
Semigroup Kernels on Finite Sets
Complex objects can often be conveniently represented by finite sets of simpler components, such as images by sets of patches or texts by bags of words. We study the class of posi...
Marco Cuturi, Jean-Philippe Vert