Speckle Accelerator for Randomized NLA

Under one aspect, a method for performing a linear algebra operation includes imposing matrix elements onto a chirped optical carrier; inputting into a multi-mode optic the matrix elements imposed on the chirped optical carrier; outputting by the multi-mode optic a speckle pattern based on the matrix elements imposed on the optical carrier; and performing a linear algebra operation on the matrix elements based on the speckle pattern. The matrix elements can be from matrix A and a vector b, and the multi-mode optic can optically transform each of matrix A and vector b by a speckle transformation S, so as to output a speckle pattern including elements of a matrix SA of dimension p,n and matrix elements of a vector Sb of dimension p. The linear algebra operation can include generating {tilde over (x)}=(SA).sup..dagger.Sb, wherein .dagger. indicates a pseudo-inverse operation.