An extension to adaptive signal subspace methods is presented, based on singular value decomposition (SVD) with an online estimation of the noise variance. With this approach aiming at automatic speech recognition (ASR) in adverse environmental conditions no speech detection has to be performed. A comparison of different SVD approaches and nonlinear spectral subtraction within ASR experiments o...

State-of-the-art methods for learning unions of subspaces from a collection of data leverage sparsity to form representations of each vector in the dataset with respect to the remaining vectors in the dataset. The resulting sparse representations can be used to form a subspace affinity matrix to cluster the data into their respective subspaces. While sparsity-driven methods for subspace cluster...

We present two characterizations of Lagrange interpolation sets for weak Chebyshev spaces. The rst of them is valid for an arbitrary weak Chebyshev space U and is based on an analysis of the structure of zero sets of functions in U extending Stockenberg's theorem. The second one holds for all weak Chebyshev spaces that possess a locally linearly independent basis. x1. Introduction Let U denote ...

Abstract This research apparatuses an approximate spectral method for the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel (TFPIDE). The main idea of this approach is to set up new Hilbert space that satisfies initial and boundary conditions. collocation applied obtain precise numerical approximation using basis functions based on shifted first-kind ...

Abstract The shifted Chebyshev polynomials of the fifth kind (SCPFK) and collocation method are employed to achieve approximate solutions a category functional equations, namely variable-order time-fractional weakly singular partial integro-differential equations (VTFWSPIDEs). A pseudo-operational matrix (POM) approach is developed for numerical solution problem under study. suggested changes s...

An infinite Markov system {f0, f1, . . . } of C2 functions on [a, b] has dense span in C[a, b] if and only if there is an unbounded Bernstein inequality on every subinterval of [a, b]. That is if and only if, for each [α, β] ⊂ [a, b] and γ > 0, we can find g ∈ span{f0, f1, . . . } with ‖g′‖[α,β] > γ‖g‖[a,b]. This is proved under the assumption (f1/f0)′ does not vanish on (a, b). Extension to hi...

We show that the space Lip0(R) is the dual space of L(R;R)/N where N is the subspace of L(R;R) consisting of vector fields whose divergence vanishes identically. We prove that although the quotient space L(R;R)/N is weakly sequentially complete, the subspace N is not nicely placed in other words, its unit ball is not closed for the topology τm of local convergence in measure. We prove that if Ω...

We show that if X is a tight subspace of C(K) then X has the Pe lczyński property and X is weakly sequentially complete. We apply this result to the space U of uniformly convergent Taylor series on the unit circle and using a minimal amount of Fourier theory prove that U has the Pe lczyński property and U is weakly sequentially complete. Using separate methods, we prove U and U have the Dunford...

Covariance inflation is one of the necessary tools enabling success ensemble Kalman filters (EnKFs) in high dimensional spaces and presence model error. Inflation maintains variance to a sufficiently large value, counteracting damping at analysis times its underestimate arising from sampling errors. In this work we investigate effect on dynamics EnKF ensemble. When focus recursive full cycle fo...