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Numerical Linear Algebra

At Berkeley Lab, we develop efficient and scalable algorithms and codes for solving large-scale linear algebra problems, which arise in scientific modeling and simulation, including sparse and dense linear systems of equations, eigenvalue computations, tensor decompositions, and more.

Our researchers work closely with scientists in the Department of Energy complex and academia to develop state-of-the-art numerical algorithms that exploit a variety of properties in data generated by numerical simulations, such as structural sparsity, data sparsity (low-rank structure), symmetry, and more. This approach allows for more accurate scientific models and simulations by providing algorithms with reduced asymptotic complexity that can scale up to previously intractable dimensions on high performance computing (HPCs) systems. Our open-source numerical linear algebra codes can scale up to thousands of computing cores on a supercomputer or run just as efficiently on a personal computer.

We are also continuously adapting our codes to ensure that they continue to run efficiently on ever-evolving HPC hardware and architectures.


SuperLU (Supernodal LU)

SuperLU is a general purpose library for the direct solution of large, sparse, nonsymmetric systems of linear equations. Contact: Xiaoye Sherry Li (Li on the Web)

STRUMPACK (STRUctured Matrix PACKage)

STRUMPACK is a software library providing linear algebra routines and linear system solvers for sparse and for dense rank-structured linear systems. Contact: Pieter Ghysels (Ghysels on the Web)

PDSLin (Parallel Domain decomposition Schur complement based Linear Solver)

Parallel domain-decomposition Schur-complement linear solver. Contact: Xiaoye Sherry Li (Li on the Web)


GPTune is an autotuning framework that relies on multitask and transfer learnings to help solve the underlying black-box optimization problem using Bayesian optimization methodologies. Contact: Xiaoye Sherry Li (Li on the Web)


ButterflyPACK is a mathematical software for rapidly solving large-scale dense linear systems that exhibit off-diagonal rank-deficiency. These systems arise frequently from boundary element methods, or factorization phases in finite-difference/finite-element methods. Contact: Yang Liu (Liu on the Web)


BSEPACK is a parallel package for solving definite Bethe–Salpeter eigenvalue problems. Contact: Chao Yang (Yang on the Web)

Quantum numerical linear algebra

Develop efficient algorithms for solving eigenvalue problems, linear systems of equations, and block encodings of sparse matrices. Contacts: Lin Lin, Chao Yang

Quantum signal processing

Develop optimization based algorithm for robust solution of phase factors in quantum signal processing, which can be used in variety of scientific computing applications. Contact: Lin Lin


QCLAB is an object-oriented software library for creating and representing quantum circuits. QCLAB can be used for rapid prototyping and testing of quantum algorithms, and allows for fast algorithm development and discovery. QCLAB provides I/O through openQASM making it compatible with quantum hardware. Contact: Roel Van Beeumen (Beeumen on the Web)


Fast Free Fermion Compiler (F3C) is a software library for compiling time-evolution quantum circuits of spin Hamiltonians that can be mapped to free fermions. Contact: Roel Van Beeumen (Beeumen on the Web)


Fast Approximate BLock Encodings (FABLE) is a software library for synthesizing quantum circuits of approximate block-encodings of matrices. A block-encoding is the embedding of a matrix in the leading block of a larger unitary matrix. Contact: Roel Van Beeumen (Beeumen on the Web)


FFTX is the exascale follow-on to the FFTW open-source discrete FFT package for executing the Fast Fourier Transform. FFTX also supports higher-level operations composed of linear operators combined with Fast Fourier Transforms. FFTX is based on the SPIRAL build-time code generator, which produces very high-performance kernels targeted to their specific uses and platform environments. Contact: Peter McCorquodale


CRD’s Lin Lin Honored with Simons Foundation Award

June 29, 2021

Lin Lin, a faculty scientist in Berkeley Lab's Mathematics Group and a mathematician in CAMERA, has been selected to receive a Simons Investigator in Mathematics award. Read More »

New Alvarez Fellow Eyes New Applications for Math and ML

September 29, 2021

Osman Malik, the newest Berkeley Lab Alvarez Fellow, joined the the Applied Math and Computational Research Division's Scalable Solvers Group on September 1. Read More »

At 14, SuperLU Solver Library Still Gaining Popularity

April 23, 2013

Since its launch in 1999, the SuperLU software library for solving sparse linear systems of equations has become the third most downloaded software at Lawrence Berkeley National Laboratory. Read More »