4 papers
SuperPCA: subspace analysis and an efficient algorithm for high-dimensional PCA
Irina-Beatrice Haas, Maike Meier, Yuji Nakatsukasa +1
Principal component analysis (PCA) is a fundamental tool to reduce the dimensionality of the data in many applications. PCA finds a few signal directions that contain most of the v…
A multilevel sketch-and-solve method for overdetermined least squares problems
Irina-Beatrice Haas, Michael B. Giles, Yuji Nakatsukasa
Sketch-and-solve (SAS) is a very successful method to efficiently estimate the solution of heavily overdetermined large linear least squares problems. It uses random sketching to r…
Sharp error bounds for approximate eigenvalues and singular values from subspace methods
Irina-Beatrice Haas, Yuji Nakatsukasa
Subspace methods are commonly used for finding approximate eigenvalues and singular values of large-scale matrices. Once a subspace is found, the Rayleigh-Ritz method (for symmetri…
A nested MLMC framework for efficient simulations on FPGAs
Irina-Beatrice Haas, Michael B. Giles
Multilevel Monte Carlo (MLMC) reduces the total computational cost of financial option pricing by combining SDE approximations with multiple resolutions. This paper explores a furt…