Simulation of Contactless Crack Detection in HTS Films: Application of <i>H</i>-Matrix Method to Fast Matrix-Vector Multiplication

Fast QMC Matrix-Vector Multiplication

Quasi-Monte Carlo (QMC) rules 1/N ∑N−1 n=0 f(ynA) can be used to approximate integrals of the form ∫ [0,1]s f(yA) dy, where A is a matrix and y is row vector. This type of integral arises for example from the simulation of a normal distribution with a general covariance matrix, from the approximation of the expectation value of solutions of PDEs with random coefficients, or from applications fr...

Fast construction of hierarchical matrix representation from matrix-vector multiplication

We develop a hierarchical matrix construction algorithm using matrix–vector multiplications, based on the randomized singular value decomposition of low-rank matrices. The algorithm uses OðlognÞ applications of the matrix on structured random test vectors and Oðn lognÞ extra computational cost, where n is the dimension of the unknown matrix. Numerical examples on constructing Green’s functions ...

Sparse Matrix-Vector Multiplication for Circuit Simulation

Sparse Matrix-Vector Multiplication (SpMV) plays an important role in numerical algorithm in circuit simulation. In this report, we utilize Message Passing Interface (MPI) to parallelize the SpMV. In addition, resulting from the circuit simulation matrix formulation, the circuit systems are often represented as unstructured, not evenly-distributed sparse matrices. Therefore, we automatically de...

Fast Matrix Multiplication

We give an overview of the history of fast algorithms for matrix multiplication. Along the way, we look at some other fundamental problems in algebraic complexity like polynomial evaluation. This exposition is self-contained. To make it accessible to a broad audience, we only assume a minimal mathematical background: basic linear algebra, familiarity with polynomials in several variables over r...

Fast matrix multiplication