Motivated by the study of singular values random rectangular matrices, we define and additive convolution polynomials with nonnegative real roots. Our definition directly generalizes asymmetric introduced Marcus, Spielman Srivastava (2015), our main theorem gives corresponding generalization bound on largest root from that paper. The tool used in analysis is a differential operator derived "rec...

We present the characterization and design of multidimensional oversampled FIR filter banks. In the polyphase domain, the perfect reconstruction condition for an oversampled filter bank amounts to the invertibility of the analysis polyphase matrix, which is a rectangular FIR matrix. For a nonsubsampled FIR filter bank, its analysis polyphase matrix is the FIR vector of analysis filters. A major...

in this paper we introduce a type of fractional-order polynomials basedon the classical chebyshev polynomials of the second kind (fcss). also we construct the operationalmatrix of fractional derivative of order $ gamma $ in the caputo for fcss and show that this matrix with the tau method are utilized to reduce the solution of some fractional-order differential equations.

 Let $P(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. In this paper, some algebraic and geometrical properties of the $k$-numerical range of $P(lambda)$ are investigated. In particular, the relationship between the $k$-numerical range of $P(lambda)$ and the $k$-numerical range of its companion linearization is stated. Moreover, the $k$-numerical...

In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.

We obtain randomized algorithms for factoring degree n univariate polynomials over Fq that use O(n + n log q) field operations, when the characteristic is at most n. When log q < n, this is asymptotically faster than the best previous algorithms (von zur Gathen & Shoup (1992) and Kaltofen & Shoup (1998)); for log q ≥ n, it matches the asymptotic running time of the best known algorithms. The im...

Abstract.In this paper, the generalized Bessel matrix polynomials are introduced, starting from the hypergeometric matrix function. Integral form, Rodrigues’s formula and generating matrix function are then developed for the generalized Bessel matrix polynomials. These polynomials appear as finite series solutions of second-order matrix differential equations and orthogonality property for the ...

We obtain randomized algorithms for factoring degree n univariate polynomials over Fq requiring O(n1.5+o(1) log q + n1+o(1) logq) bit operations. When log q < n, this is asymptotically faster than the best previous algorithms [J. von zur Gathen and V. Shoup, Comput. Complexity, 2 (1992), pp. 187–224; E. Kaltofen and V. Shoup, Math. Comp., 67 (1998), pp. 1179– 1197]; for log q ≥ n, it matches th...

in this paper, we introduce the notions of c-numerical range and c-spectrum of matrix polynomials. some algebraic and geometrical properties are investigated. we also study the relationship between the c-numerical range of a matrix polynomial and the joint c-numerical range of its coefficients.