QRT: A Qr-based tridiagonalization algorithm for nonsymmetric matrices

The stable similarity reduction of a nonsymmetric square matrix to tridiagonal form has been a long-standing problem in numerical linear algebra. The biorthogonal Lanczos process is in principle a candidate method for this task, but in practice it is confined to sparse matrices and is restarted periodically because roundoff errors affect its three-term recurrence scheme and degrade the biorthogonality after a few steps. This adds to its vulnerability to serious breakdowns or near-breakdowns, the handling of which involves recovery strategies such as the look-ahead technique, which needs a careful implementation to produce a block-tridiagonal form with unpredictable block sizes. Other candidate methods, geared generally towards full matrices, rely on elementary similarity transformations that are prone to numerical instabilities. Such concomitant difficulties have hampered finding a satisfactory solution to the problem for either sparse or full matrices. This study focuses primarily on full matrices. After outlining earlier tridiagonalization algorithms from within a general framework, we present a new elimination technique combining orthogonal similarity transformations that are stable. We also discuss heuristics to circumvent breakdowns. Applications of this study include eigenvalue calculation and the approximation of matrix functions.

QR decomposition-based matrix inversion for high performance embedded MIMO receivers

Real-time matrix inversion is a key enabling technology in multiple-input multiple-output (MIMO) communications systems, such as 802.11n. To date, however, no matrix inversion implementation has been devised which supports real-time operation for these standards. In this paper, we overcome this barrier by presenting a novel matrix inversion algorithm which is ideally suited to high performance floating-point implementation. We show how the resulting architecture offers fundamentally higher performance than currently published matrix inversion approaches and we use it to create the first reported architecture capable of supporting real-time 802.11n operation. Specifically, we present a matrix inversion approach based on modified squared Givens rotations (MSGR). This is a new QR decomposition algorithm which overcomes critical limitations in other QR algorithms that prohibits their application to MIMO systems. In addition, we present a novel modification that further reduces the complexity of MSGR by almost 20%. This enables real-time implementation with negligible reduction in the accuracy of the inversion operation, or the BER of a MIMO receiver based on this.

On computing an equivalent symmetric matrix for a nonsymmetric matrix

A real or a complex symmetric matrix is defined here as an equivalent symmetric matrix for a real nonsymmetric matrix if both have the same eigenvalues. An equivalent symmetric matrix is useful in computing the eigenvalues of a real nonsymmetric matrix. A procedure to compute equivalent symmetric matrices and its mathematical foundation are presented.

An optimal parallel algorithm for sparse matrix bandwidth reduction on a linear array

A simple and efficient algorithm for the bandwidth reduction of sparse symmetric matrices is proposed. It involves column-row permutations and is well-suited to map onto the linear array topology of the SIMD architectures. The efficiency of the algorithm is compared with the other existing algorithms. The interconnectivity and the memory requirement of the linear array are discussed and the complexity of its layout area is derived. The parallel version of the algorithm mapped onto the linear array is then introduced and is explained with the help of an example. The optimality of the parallel algorithm is proved by deriving the time complexities of the algorithm on a single processor and the linear array.

In situ synthesis of Al2O3-ZrO2-SiCW ceramic matrix composites by carbothermal reduction of natural silicates

In situ formations of Al2O3 + ZrO2 + SiCW ternary composite powders have been obtained by carbothermal reduction of a mixture of Sillimanite. Kaolin and Zircon using two different carbon sources. Products formed were mixtures of alumina and zirconia along with silicon carbide in the form of whiskers. The effects of composition of the reactants, the role of fineness of the starting precursors and the nature of the carbon Source on the final product powder obtained are presented. XRD and SEM analyses indicate complete reaction of the precursors to yield Al2O3 + ZrO2 + SiCW as product powders, with the SiC having whisker morphology. It is also seen that zirconia could be stabilised to some extent in the tetragonal form without any stabilising agent by tailoring the starting materials and their composition. (C) 2002 Published by Elsevier Science B.V.

Reduction of severe bovine serum associated matrix effects on carboxymethylated dextran coated biosensor surfaces

Surface plasmon resonance (SPR) based biosensor technology has been widely used in life science research for many applications. While the advantages of speed, ruggedness, versatility, sensitivity and reproducibility are often quoted, many researchers have experienced severe problem of non-specific binding (NSB) to chip surfaces when performing analysis of biological samples Such as bovine serum. Using the direct measurement of the bovine protein leptin, present in bovine serum samples as a model, a unique buffering system has been developed and optimised which was able to significantly reduce the non-specific interactions of bovine serum components with the carboxymethyl dextran chip (CM5) surface on a Biacore SPR The developed NSB buffering system comprised of HBS-EP buffer, containing 0.5 M NaCl, 0.005% CM-dextran pH 9.0. An average NSB reduction (n = 20) of 85.9% and 87.3% was found on an unmodified CM5 surface and a CM5 with bovine leptin immobilised on the chip surface, respectively. A reduction in NSB of up to 94% was observed on both surfaces. The concentration of the constitutive components and pH of the buffer were crucial in achieving this outcome. (C) 2008 Elsevier B.V. All rights reserved.

Reduction of sample matrix effects - The analysis of benzimidazole residues in serum by immunobiosensor

Regulatory authorities, the food industry and the consumer demand reliable determination of chemical contaminants present in foods. A relatively new analytical technique that addresses this need is an immunobiosensor based on surface plasmon resonance (SPR) measurements. Although a range of tests have been developed to measure residues in milk, meat, animal bile and honey, a considerable problem has been encountered with both serum and plasma samples. The high degree of non-specific binding of some sample components can lead to loss of assay robustness, increased rates of false positives and general loss of assay sensitivity. In this paper we describe a straightforward precipitation technique to remove interfering substances from serum samples to be analysed for veterinary anthelmintics by SPR. This technique enabled development of an assay to detect a wide range of benzimidazole residues in serum samples by immunobiosensor. The limit of quantification was below 5 ng/ml and coefficients of variation were about 2%.

REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.

Ribozyme-mediated reduction of wild-type and mutant cartilage oligomeric matrix protein (COMP) mRNA and protein.

Dominant-negative mutations in the homopentameric extracellular matrix glycoprotein cartilage oligomeric matrix protein (COMP) result in inappropriate intracellular retention of misfolded COMP in the rough endoplasmic reticulum of chondrocytes, causing chondrocyte cell death, which leads to two skeletal dysplasias: pseudoachondroplasia (PSACH) and multiple epiphyseal dysplasia (EDM1). COMP null mice show no adverse effects on normal bone development and growth, suggesting a possible therapy involving removal of COMP mRNA. The goal of this study was to assess the ability of a hammerhead ribozyme (Ribo56, designed against the D469del mutation) to reduce COMP mRNA expression. In COS7 cells transfected with plasmids that overexpress wild-type or mutant COMP mRNA and Ribo56, the ribozyme reduced overexpressed normal COMP mRNA by 46% and mutant COMP mRNA by 56% in a dose-dependent manner. Surprisingly, the use of recombinant adenoviruses to deliver wild-type or mutant COMP mRNA and Ribo56 simultaneously into COS7 cells proved problematic for the activity of the ribozyme to reduce COMP expression. However, in normal human costochondral cells (hCCCs) infected only with adenoviruses expressing Ribo56, expression of endogenous wild-type COMP mRNA was reduced in a dose-dependent manner by 50%. In chondrocytes that contain heterozygous COMP mutations (D469del, G427E and D511Y) that cause PSACH, Ribo56 was more effective at reducing COMP mRNA (up to 70%). These results indicate that Ribo56 is effective at reducing mutant and wild-type COMP levels in cells and suggests a possible mode of therapy to reduce the mutant protein load.