Methods for stochastic trace estimation often require the repeated evaluation of expressions form zTpn(A)z, where A is a symmetric matrix and pn degree n polynomial written in standard or Chebyshev basis. We show how to evaluate these using only ⌈n∕2⌉ matrix–vector products, thus substantially reducing cost existing algorithms that use interpolation Taylor series.

We give complexity estimates for the problems of evaluation and interpolation on various polynomial bases. We focus on the particular cases when the sample points form an arithmetic or a geometric sequence, and we discuss applications, respectively to computations with linear differential operators and to polynomial matrix multiplication.

A novel linear transform (LT) is proposed for frequency warping (FW) with standard filterbank based MFCC features. Here, we use the idea of spectral interpolation of [9] to perform a continuous warping in the log filterbank output domain, and incorporate both interpolation and warping into a single warped IDCT matrix. The new transformation matrix is thus mathematically simpler than in [9], and...

In our previous study, we proposed the waveform interpolation (WI) approach to model the excitation signals for hidden Markov model (HMM)-based speech synthesis. This letter presents several techniques to improve excitation modeling within the WI framework. We propose both the time domain and frequency domain zero padding techniques to reduce the spectral distortion inherent in the synthesized ...

The author presents a polynomial-based algorithm for high-order multidimensional interpolation at the coarse-fine interface in the context of adaptive mesh refinement on structured Cartesian grids. The proposed algorithm reduces coarse-fine interpolation to matrix-vector products by exploiting the static mesh geometry and a family of nonsingularity-preserving stencil transformations. As such, n...

This work presents a novel least squares matrix algorithm (LSM) for the analysis of rapidly changing systems using state-space modelling. The LSM algorithm is based on the Hankel structured data matrix representation. The state transition matrix is updated without the use of any forgetting function. This yields a robust estimation of model parameters in the presence of noise. The computational ...

The article describes a flexible mapping technique realized as a many-to-many dynamic mapping matrix. Digital sound generation is typically controlled by a large number of parameters and efficient and flexible mapping is necessary to provide expressive control over the instrument. The proposed modulation matrix technique may be seen as a generic and selfmodifying mapping mechanism integrated in...

Generalized matrix functions (GMFs) extend the concept of a matrix function to rectangular matrices via the singular value decomposition. Several applications involving directed graphs, Hamiltonian dynamical systems, and optimization problems with low-rank constraints require the action of a GMF of a large, sparse matrix on a vector. We present a new method for applying GMFs to vectors based on...

In this note, we solve an inverse spectral problem for a class of finite band symmetric matrices. We provide necessary and sufficient conditions for a matrix valued function to be a spectral function of the operator corresponding to a matrix in our class and give an algorithm for recovering this matrix from the spectral function. The reconstructive algorithm is applicable to matrices which cann...