This paper proposes a new Levenberg-Marquardt algorithm that is accelerated by adjusting a Jacobian matrix and a quasi-Hessian matrix. The proposed method partitions the Jacobian matrix into block matrices and employs the inverse of a partitioned matrix to find the inverse of the quasi-Hessian matrix. Our method can avoid expensive operations and save memory in calculating the inverse of the qu...

In this paper, we present a framework for synthesizing I/O eecient out-of-core programs for block recursive algorithms, such as the fast Fourier transform (FFT) and block matrix transposition algorithms. Our framework uses an algebraic representation which is based on tensor products and other matrix operations. The programs are optimized for the striped Vitter and Shriver's two-level memory mo...

This paper describes Householder reduction of a rectangular sparse matrix to small band upper triangular form Bk+1. Bk+1 is upper triangular with nonzero entries only on the diagonal and on the nearest k superdiagonals. The algorithm is similar to the Householder reduction used as part of the standard dense SVD computation. For the sparse “lazy” algorithm, matrix updates are deferred until a ro...

We discuss a generalization of the Cohn–Umans method, a potent technique developed for studying the bilinear complexity of matrix multiplication by embedding matrices into an appropriate group algebra. We investigate how the Cohn–Umans method may be used for bilinear operations other than matrix multiplication, with algebras other than group algebras, and we relate it to Strassen’s tensor rank ...

We consider saddle-point problems that typically arise from the mixed finite element discretization of second order elliptic problems. By proper equivalent algebraic operations the considered saddle-point problem is transformed to another saddle-point problem. The resulting problem can then be efficiently preconditioned by a block-diagonal matrix or by a factored block-matrix (the blocks corres...

We study how to obtain partial matchings using the block function Mf, induced by a morphism f between persistence modules. Mf is defined algebraically and linear with respect direct sums of morphisms. some interesting properties provide way obtaining matrix operations.

This paper studies systems of explicit mathematics as introduced by Feferman [9, 11]. In particular, we propose weak explicit type systems with a restricted form of elementary comprehension whose provably terminating operations coincide with the functions on binary words that are computable in polynomial time. The systems considered are natural extensions of the first-order applicative theories...

Since the discovery of the "Philadelphia chromosome" in chronic myelogenous leukemia in 1960, there has been ongoing intensive research of chromosomal aberrations in cancer. These aberrations, which result in abnormally structured genomes, became a hallmark of cancer. Many studies provide evidence for the connection between chromosomal alterations and aberrant genes involved in the carcinogenes...

The theory of compressed sensing tells us that recovering all k-sparse signals requires a sensing matrix to satisfy that its spark is greater than 2k, or its order of the null space property (NSP) or the restricted isometry property (RIP) is 2k or above. If we perform elementary row or column operations on the sensing matrix, what are the changes of its spark, NSP order and RIP order? In this p...

A programming environment combines elementary operations into single composite operations to be applied by the user. The operands of the composite operation may be decomposed, their components processed by elementary operations, the results combined in arbitrary ways and manipulated by other elementary operations, and a final product delivered to the user. If one of the elementary operations de...