Related papers: Fast Differentiable Matrix Square Root and Inverse…
This paper addresses the positive semi-definite procrustes problem (PSDP). The PSDP corresponds to a least squares problem over the set of symmetric and semi-definite positive matrices. These kinds of problems appear in many applications…
Circumstellar disk images have highlighted a wide variety of morphological features. Recovering disk images from high-contrast angular differential imaging (ADI) sequences are however generally affected by geometrical biases, leading to…
In this paper we present an efficient iterative method of order six for the inclusion of the inverse of a given regular matrix. To provide the upper error bound of the outer matrix for the inverse matrix, we combine point and interval…
Recent advances in neural-network architecture allow for seamless integration of convex optimization problems as differentiable layers in an end-to-end trainable neural network. Integrating medium and large scale quadratic programs into a…
Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction…
Fast approximations to matrix multiplication have the potential to dramatically reduce the cost of neural network inference. Recent work on approximate matrix multiplication proposed to replace costly multiplications with table-lookups by…
The article considers linear functions of many (n) variables - multilinear polynomials (MP). The three-steps evaluation is presented that uses the minimal possible number of floating point operations for non-sparse MP at each step. The…
The need to compute the intersections between a line and a high-order curve or surface arises in a large number of finite element applications. Such intersection problems are easy to formulate but hard to solve robustly. We introduce a…
Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…
The Forward-Forward (FF) algorithm was recently proposed as a local learning method to address the limitations of backpropagation (BP), offering biological plausibility along with memory-efficient and highly parallelized computational…
Schur's transforms of a polynomial are used to count its roots in the unit disk. These are generalized them by introducing the sequence of symmetric sub-resultants of two polynomials. Although they do have a determinantal definition, we…
Many neural learning algorithms require to solve large least square systems in order to obtain synaptic weights. Moore-Penrose inverse matrices allow for solving such systems, even with rank deficiency, and they provide minimum-norm vectors…
In this work we are interested in general linear inverse problems where the corresponding forward problem is solved iteratively using fixed point methods. Then one-shot methods, which iterate at the same time on the forward problem solution…
We use the well-known observation that the solutions of Jacobi's differential equation can be represented via non-oscillatory phase and amplitude functions to develop a fast algorithm for computing multi-dimensional Jacobi polynomial…
Data-driven decision-making processes increasingly utilize end-to-end learnable deep neural networks to render final decisions. Sometimes, the output of the forward functions in certain layers is determined by the solutions to mathematical…
Forward scatter radar (FSR) has emerged as an effective imaging modality for target detection, utilizing forward scattering (FS) signals to reconstruct two-dimensional shadow profile images of objects. However, real-world FS signals are…
Inverse path tracing has recently been applied to joint material and lighting estimation, given geometry and multi-view HDR observations of an indoor scene. However, it has two major limitations: path tracing is expensive to compute, and…
The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering tasks. Unfortunately, designing fast algorithms for the…
Square matrices of the form $\widetilde{\mathbf{A}} =\mathbf{A} + \mathbf{e}D \mathbf{f}^*$ are considered. An explicit expression for the inverse is given, provided $\widetilde{\mathbf{A}}$ and $D$ are invertible with…
In several papers of 2013 - 2016, Guglielmi and Protasov made a breakthrough in the problem of the joint spectral radius computation, developing the invariant polytope algorithm which for most matrix families finds the exact value of the…