Solvers

Dominant Eigenpair Computation

LMSVD is an adaptive Krylov subspace algorithm for dominant singular value decomposition.

Code: MATLAB File Exchange
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Reference:
Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions (SIAM Journal on Scientific Computing).

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SLRP is a Gauss Newton method of symmetric low-rank product for calculating dominant eigenspace.

Code: two lines in MATLAB (Please see to the left.)

Reference:
An Efficient Gauss-Newton Algorithm for Symmetric Low-Rank Product Matrix Approximations (SIAM Journal on Optimization).

Optimization Problems with Orthognality Constraints

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FOForth is a first-order framework for solving optimization problems with orthognality constraints, including three algorithms: gradient reflection, gradient projection and column-wise block coordinate descend.

Code: MATLAB File Exchange

Reference:
A First-Order Framework for optimization problems with orthogonality constraints (SIAM Journal on Optimization).

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PCAL is a parallelizable approach for solving optimization problems with orthognality constraints.

Code: MATLAB File Exchange

Reference:
Parallelizable Column-wise Augmented Lagrangian approaches for optimization with orthogonality constraints (SIAM Journal on Scientific Computing).