In this paper design of low pass optimal block digital filter is compared with traditional low pass overlap-save block digital filter. Simulation results show that global error obtained by optimal method is lower than that obtained by traditional overlap-save method. Index Terms Block digital filters, optimum design, overlap-save method, frobenius norm, aliasing, time-varying system.

2 Linear Algebra 3 2.1 Basics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Norms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Vector norms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Induced matrix norms. . . . . . . . . . . . . . . . . . . . . . . . ....

Singular value decomposition (SVD) is one of the most useful matrix decompositions in linear algebra. Here, a novel application SVD recovering ripped photos was exploited. Recovery done by applying truncated iteratively. Performance evaluated using Frobenius norm. Results from few experimental were decent.

it is well known that if the coefficient matrix in a linear system is large and sparse or sometimes not readily available, then iterative solvers may become the only choice. the block solvers are an attractive class of iterative solvers for solving linear systems with multiple right-hand sides. in general, the block solvers are more suitable for dense systems with preconditioner. in this paper,...

A few iterations of alternating least squares with a random starting point provably suffice to produce nearly optimal spectraland Frobenius-norm accuracies of low-rank approximations to a matrix; iterating to convergence is unnecessary. Thus, software implementing alternating least squares can be retrofitted via appropriate setting of parameters to calculate nearly optimally accurate low-rank a...

In this paper we give an explicit solution to the rank constrained matrix approximation in Frobenius norm, which is a generalization of the classical approximation of an m× n matrix A by a matrix of rank k at most. 2000 Mathematics Subject Classification: 15A18.

It is a well-known fact that the Krylov space K j ( H , x ) generated by skew-Hamiltonian matrix ? R 2 n × and some isotropic for any N . For given subspace L ? of dimension —which called Lagrangian subspace—the question whether can be as considered. The affine variety HK all matrices generate analyzed. Existence uniqueness results are proven, found with minimal 2-norm, Frobenius norm prescribe...

The problem of updating damped gyroscopic systems using measured modal data can be mathematically formulated as following two problems. Problem I: Given Ma ∈ Rn×n,Λ = diag{λ1, · · · , λp} ∈ Cp×p, X = [x1, · · · , xp] ∈ Cn×p, where p < n and both Λ and X are closed under complex conjugation in the sense that λ2j = λ̄2j−1 ∈ C, x2j = x̄2j−1 ∈ C for j = 1, · · · , l, and λk ∈ R, xk ∈ R for k = 2l+1, ...

In this paper, a new test statistic based on the weighted Frobenius norm of covariance matrices is proposed to homogeneity multi-group population matrices. The asymptotic distributions under null and alternative hypotheses are derived, respectively. Simulation results show that procedure tends outperform some existing procedures.

Abstract. We consider here the linear least squares problem miny∈Rn ‖Ay− b‖2, where b ∈ Rm and A ∈ Rm×n is a matrix of full column rank n, and we denote x its solution. We assume that both A and b can be perturbed and that these perturbations are measured using the Frobenius or the spectral norm for A and the Euclidean norm for b. In this paper, we are concerned with the condition number of a l...