Templates for the Solution of Algebraic Eigenvalue Problems

By J. Demmel, Jack J. Dongarra, Axel Ruhe, Henk A. van der Vorst, Zhong-Zhi Bai. Software, environments, tools, 2000

1,679 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/0fbf98f1fec4d33c4fc615655d2cfc1968cb1cf4

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In Computational Theory and Mathematics

Citations in the corpus

octopus: a tool for the application of time‐dependent density functional theory (2006, background): “The literature in this field is abundant [ 22 ], and we have tried several schemes in octopus.”
MARVEL: Measured active rotational–vibrational energy levels. II. Algorithmic improvements☆ (2012, methodology): “The compressed row and column storage (CRS and CCS) formats [55] are the most generally used storage methods for sparse matrices.”
On 3D modeling of seismic wave propagation via a structured parallel multifrontal direct Helmholtz solver (2011, methodology): “Unlike the classical LU factorization, such a factorization method is a left-looking method (Bai et al. 2000), where there is no global Schur complement computation.”
Adaptive blind signal and image processing (2002, background): “Another efficient and fast algorithms for the eigenvalue problems the reader can find in the excellent book [62].”
Joint Communication and Control for Wireless Autonomous Vehicular Platoon Systems (2018, methodology): “Note that matrices in the numerator and denominator of (13) are symmetric, and, hence, we can use the inverse iteration algorithm and power iteration algorithm, introduced in [33], to approximately find the minimum eigenvalue for the matrix in the numerator and the maximum eigenvalue for the matrix ”
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems (2005, background): “Methods for sparse eigenproblems [Bai et al. 2000] usually obtain the solution from the information generated by the application of the matrix to various vectors.”
Sparsity: Optimization Framework for Sparse Matrix Kernels (2004, methodology): “/* loop over block rows */ 1 for( i = 0; i < bm; i++, y += 2 ) { 2 register double d0 = y[0]; 3 register double d1 = y[1]; 4 for( jj = b_row_start[i]; jj < b_row_start[i+1]; jj++, b_col_idx++, b_value += 2*2 ) { 5 d0 += b_value[0] * x[b_col_idx[0]+0]; 6 d1 += b_value[2] * x[b_col_idx[0]+0]; 7 d0 += ”
A numerical method for polynomial eigenvalue problems using contour integral (2010, background): “The PEP [ 1 ,6,9] involves finding an eigenvalue λ and corresponding nonzero eigenvector x that satisfy F(λ)x = 0, where F(λ) = � l=0 λ i Ai”
Preconditioned Low-Rank Methods for High-Dimensional Elliptic PDE Eigenvalue Problems (2011, methodology): “This excludes the use of classical iterative methods [1, 6] already for moderate values of d.”