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Symmetric Positive Definite Systems
, 2008
"... Use datadependent linear function space P f (x) = N∑ cjΦ(x, x j), j=1 x ∈ R s Here Φ: R s × R s → R is strictly positive definite (reproducing) kernel ..."
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Use datadependent linear function space P f (x) = N∑ cjΦ(x, x j), j=1 x ∈ R s Here Φ: R s × R s → R is strictly positive definite (reproducing) kernel
Computing the Logarithm of a Symmetric Positive Definite Matrix
 Appl. Numer. Math
"... A numerical method for computing the logarithm of a symmetric positive definite matrix is developed in this paper. It is based on reducing the original matrix to a tridiagonal matrix by orthogonal similarity transformations and applying Pad'e approximations to the logarithm of the tridiagonal m ..."
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Cited by 3 (2 self)
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A numerical method for computing the logarithm of a symmetric positive definite matrix is developed in this paper. It is based on reducing the original matrix to a tridiagonal matrix by orthogonal similarity transformations and applying Pad'e approximations to the logarithm of the tridiagonal
APPROXIMATING THE INVERSE OF A SYMMETRIC POSITIVE DEFINITE MATRIX
"... It is shown for an n \Theta n symmetric positive definite matrix T = (t i;j ) with negative offdiagonal elements, positive row sums and satisfying certain bounding conditions that its inverse is well approximated, uniformly to order 1=n 2 ; by a matrix S = (s i;j ); where s i;j = ffi i;j =t i;i ..."
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It is shown for an n \Theta n symmetric positive definite matrix T = (t i;j ) with negative offdiagonal elements, positive row sums and satisfying certain bounding conditions that its inverse is well approximated, uniformly to order 1=n 2 ; by a matrix S = (s i;j ); where s i;j = ffi i;j =t i
Image Analysis on Symmetric Positive Definite Manifolds
"... Over the last two decades, the research community has witnessed extensive research growth in the field of analysing and understanding scenes. Automatic scene analysis can support many critical applications, from person reidentification as an advanced security tool, to realtime action classificati ..."
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symmetric positive definite (SPD) matrices which form connected Riemannian manifolds.
symmetric positive definite matrices for a hypercube
, 1990
"... algorithms for the numerical factorization of large ..."
Symmetric Positive Definite Based Preconditioners For Discrete Convectiondiffusion Problems
"... Abstract — We experimentally examine the performance of preconditioners based on entries of the symmetric positive definite part and small subspace solvers for linear system of equations obtained from the highorder compact discretization of convectiondiffusion equations. Numerical results are desc ..."
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Abstract — We experimentally examine the performance of preconditioners based on entries of the symmetric positive definite part and small subspace solvers for linear system of equations obtained from the highorder compact discretization of convectiondiffusion equations. Numerical results
Symmetric positivedefinite constitutive matrices for discrete eddycurrent problems
 IEEE Transactions on Magnetics
"... We examine the construction of a symmetric positive definite conductance matrix for eddycurrent problems, using a discrete approach. We construct a new set of piecewise uniform basis vector functions on both the primal and the dual complex. We define these vector functions for both tetrahedra and ..."
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Cited by 6 (3 self)
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We examine the construction of a symmetric positive definite conductance matrix for eddycurrent problems, using a discrete approach. We construct a new set of piecewise uniform basis vector functions on both the primal and the dual complex. We define these vector functions for both tetrahedra
Directionpreserving and Schurmonotonic semiseparable approximations of symmetric positive definite matrices
 SIAM J. Matrix Anal. Appl
"... Abstract. For a given symmetric positive definite matrix A ∈ R N×N, we develop a fast and backward stable algorithm to approximate A by a symmetric positive definite semiseparable matrix, accurate to a constant multiple of any prescribed tolerance. In addition, this algorithm preserves the product, ..."
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Cited by 2 (1 self)
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Abstract. For a given symmetric positive definite matrix A ∈ R N×N, we develop a fast and backward stable algorithm to approximate A by a symmetric positive definite semiseparable matrix, accurate to a constant multiple of any prescribed tolerance. In addition, this algorithm preserves the product
AN IMPROVED SYMMETRIC POSITIVEDEFINITE FINITE ELEMENT METHOD FOR THE COMPLEX HELMHOLTZ EQUATION
"... Abstract. Most discretizations of the Helmholtz equation result in a system of linear equations that has an indefinite coefficient matrix. Much effort has been put into solving such systems of equations efficiently. In a previous work, the current author and D.C. Dobson proposed a numerical method f ..."
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for solving the complex Helmholtz equation based on the minimization variational principles developed by Milton, Seppecher, and Bouchitté. This method results in a system of equations with a symmetric positive definite coefficient matrix, but at the same time requires solving simultaneously for the solution
Results 1  10
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2,832,265