109 citations · 139 across the 14 of their papers we have counts for
8 papers · 1 filter
UltimateKalman: Flexible Kalman Filtering and Smoothing Using Orthogonal Transformations
Sivan Toledo
UltimateKalman is a flexible linear Kalman filter and smoother implemented in three popular programming languages: MATLAB, C, and Java. UltimateKalman is a slight simplification an…
Lecture Notes on Support Preconditioning
Sivan Toledo
These are lectures notes on support preconditioning, originally written in 2007. The notes cover large sparse linear systems of equations, krylov subspace solvers for symmetric dia…
High-Performance Algorithms for Computing the Sign Function of Triangular Matrices
Vadim Stotland, Oded Schwartz, Sivan Toledo
Algorithms and implementations for computing the sign function of a triangular matrix are fundamental building blocks in algorithms for computing the sign of arbitrary square real…
Wilkinson's Inertia-Revealing Factorization and Its Application to Sparse Matrices
Alex Druinsky, Eyal Carlebach, Sivan Toledo
We propose a new inertia-revealing factorization for sparse symmetric matrices. The factorization scheme and the method for extracting the inertia from it were proposed in the 1960…
Spectral Condition-Number Estimation of Large Sparse Matrices
Haim Avron, Alex Druinsky, Sivan Toledo
We describe a randomized Krylov-subspace method for estimating the spectral condition number of a real matrix A or indicating that it is numerically rank deficient. The main diffic…
How Accurate is inv(A)*b?
Alex Druinsky, Sivan Toledo
Several widely-used textbooks lead the reader to believe that solving a linear system of equations Ax = b by multiplying the vector b by a computed inverse inv(A) is inaccurate. Vi…
Effective Stiffness: Generalizing Effective Resistance Sampling to Finite Element Matrices
Haim Avron, Sivan Toledo
We define the notion of effective stiffness and show that it can used to build sparsifiers, algorithms that sparsify linear systems arising from finite-element discretizations of P…
On Element SDD Approximability
Haim Avron, Gil Shklarski, Sivan Toledo
This short communication shows that in some cases scalar elliptic finite element matrices cannot be approximated well by an SDD matrix. We also give a theoretical analysis of a sim…