Jorge Sastre Martínez

Universitat Politècnica de València | UPV · Institute of Telecommunications and Multimedia Applications (iTEAM)

The emergence of the Metaverse is raising important questions in the field of human–machine interaction that must be addressed for a successful implementation of the new paradigm. Therefore, the exploration and integration of both technology and human interaction within this new framework are needed. This paper describes an innovative and technical...

The matrix logarithm function has applicability in many engineering and science fields. Improvements in its calculation, from the point of view of both accuracy and/or execution time, have a direct impact on these disciplines. This paper describes a new numerical algorithm devoted to matrix logarithm computation and using the Romberg integration me...

Interactive computer-based music systems form a rich area for the exploration of collaborative systems where sensors play an active role and are important to the design process. The Soundcool system is a collaborative and educational system for sound and music creation as well as multimedia scenographic projects, allowing students to produce and mo...

In this paper we give a new formula to write the forward error of Taylor approximations of analytical functions in terms of the backward error of those approximations, considering exact arithmetic in both errors. Using this formula, a method to compute a backward error given by the power series centered in the same expansion point as the Taylor app...

The action of the matrix exponential on a vector eAtv, A∈Cn×n, v∈Cn, appears in problems that arise in mathematics, physics, and engineering, such as the solution of systems of linear ordinary differential equations with constant coefficients. Nowadays, several state-of-the-art approximations are available for estimating this type of action. In thi...

Creatividad audiovisual en tiempo real, colaborativa y a distancia. Con estas pocas palabras se resumen las principales características que el proyecto Soundcool ha alcanzado integrar en su sistema informático, transformando el "aquí y en este momento" en "en cualquier sitio en este momento". Real time audiovisual creation, collaborative and at a...

Hyperbolic Matrix functions cosh (A) and sinh (A) emerge in various areas of science and technology, and its computation has attracted significant attention due to their usefulness in the solution of systems of second-order linear differential equations. In this work, we introduce Bernoulli matrix polynomial series expansions for hyperbolic matrix...

The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Padé approximation, sometimes accompanied by the Schur decomposition. In this work, we present a Taylor series algorithm, based on the free-transformation approach of the inverse scaling and squaring technique...

Soundcool is a system for musical, sound and visual collaborative creation through mobile phones, tablets and other interfaces. This paper describes the creation of the app from the outset, illustrating not only how the Soundcool® system has been developed from the initial idea to the current reality, but also the evolution that the app has had dur...

Recently, two general methods for evaluating matrix polynomials requiring one matrix product less than the Paterson–Stockmeyer method were proposed, where the cost of evaluating a matrix polynomial is given asymptotically by the total number of matrix product evaluations. An analysis of the stability of those methods was given and the methods have...

Soundcool Online is a Web Audio re-implementation of the original Max/MSP implementation of Soundcool, a system for collaborative music and audiovisual creation. Soundcool has many educational applications, and because Linux has been adopted in many school systems, we turned to Web Audio to enable Soundcool to run on Linux as well as many other pla...

In this paper, we introduce two approaches to compute the matrix hyperbolic tangent. While one of them is based on its own definition and uses the matrix exponential, the other one is focused on the expansion of its Taylor series. For this second approximation, we analyse two different alternatives to evaluate the corresponding matrix polynomials....

Soundcool is a flexible, modular computer music software system created for music education. Moreover, Soundcool is an educational approach that embraces collaboration and discovery in which the teacher serves as a mentor for project based learning. To enable collaboration, Soundcool was designed from the beginning to allow individual modules to be...

Soundcool is a flexible, modular computer music software system created for music education. Moreover, Soundcool is an educational approach that embraces collaboration and discovery in which the teacher serves as a mentor for project-based learning. To enable collaboration, Soundcool was designed from the beginning to allow individual modules to be...

This article presents a free framework for collaborative creation of interactive and experimental computer music called Soundcool. It is designed to fill a gap between rigid ready-to-use applications and flexible programming languages. The system offers easy-to-use elements for generating and processing sound, much like ready-made applications, but...

This work deals with the simulation of a two‐dimensional ideal lattice having simple tetragonal geometry. The harmonic character of the oscillators give rise to a system of second‐order linear differential equations, which can be recast into matrix form. The explicit solutions which govern the dynamics of this system can be expressed in terms of ma...

Soundcool is a free system for musical, sound and visual collaborative creation through mobile phones, tablets and other interfaces developed by the Performing Arts and Technology Group (PerformingARTech) of the Universitat Politècnica de València (UPV) with the collaboration of Carnegie Mellon University. The PerformingARTech group is a multidisci...

The Group of High Performance Scientific Computing is a research group dedicated to scientific and high performance computing and its applications. We present here their main contributions to the calculation of matrix functions: mixed rational/polynomial approximations, a general family of methods for the computation of matrix polynomials which is...

In this work we introduce a new method to compute the matrix cosine. It is based on recent new matrix polynomial evaluation methods for the Taylor approximation and a mixed forward and backward error analysis. The matrix polynomial evaluation methods allow to evaluate the Taylor polynomial approximation of the matrix cosine function more efficientl...

This paper presents an implementation of one of the most up-to-day algorithms proposed to compute the matrix trigonometric functions sine and cosine. The method used is based on Taylor series approximations which intensively uses matrix multiplications. To accelerate matrix products, our application can use from one to four NVIDIA GPUs by using the...

In this work we introduce new rational-polynomial Hermite matrix expansions which allow us to obtain a new accurate and efficient method for computing the matrix cosine. This method is compared with other state-of-the-art methods for computing the matrix cosine, including a method based on Padé approximants, showing a far superior efficiency, and h...

In this paper we show new algorithms for computing hyperbolic matrix sine and cosine approximations using Hermite matrix Series Expansions

This paper presents new Taylor algorithms for the computation of the matrix exponential based on recent new matrix polynomial evaluation methods. Those methods are more efficient than the well known Paterson–Stockmeyer method. The cost of the proposed algorithms is reduced with respect to previous algorithms based on Taylor approximations. Tests ha...

In this work an accurate and efficient method based on matrix splines for computing matrix exponential is given. An algorithm and a MATLAB im- plementation have been developed and compared with the state-of-the-art algorithms for computing the matrix exponential. We also developed a par- allel implementation for large scale problems. This implement...

In this work we introduce a new method to compute the matrix cosine. It is based on recent new matrix polynomial evaluation methods for the Taylor approximation and forward and backward error analysis. The matrix polynomial evaluation methods allow to evaluate the Taylor polynomial approximation of the cosine function more efficiently than using Pa...

Music has the ability to bring people together, to facilitate the sharing of common emotions by making us feel socially members of a Community. In the case of those people affected by an intellectual disability, music can be a great support to happiness, to contribute to live better together with others, relatives or friends, as well as to facilita...

This paper addresses four criteria that the Soundcool project meets: to “be sustainable”, “be future-oriented”, “be transformative” and “be innovative”. Soundcool is a pedagogical and technological project. A brief description of the technology behind Soundcool will be useful for the reader before addressing the four criteria. Soundcool is like a “...

The computation of matrix trigonometric functions has received remarkable attention in the last decades due to its usefulness in the solution of systems of second order linear differential equations. Several state-of-the-art algorithms have been provided recently for computing these matrix functions. In this work, we present two efficient algorithm...

This paper presents a new family of methods for evaluating matrix polynomials more efficiently than the state-of-the-art Paterson–Stockmeyer method. Examples of the application of the methods to the Taylor polynomial approximation of matrix functions like the matrix exponential and matrix cosine are given. Their efficiency is compared with that of...

Computational and Mathematical Methods in Science and Engineering,

Trigonometric matrix functions play a fundamental role in second order differential equations. This work presents an algorithm based on Taylor series for computing the matrix cosine. It uses a backward error analysis with improved bounds. Numerical experiments show that MATLAB implementations of this algorithm has higher accuracy than other MATLAB...

Matrix functions have multiple applications in different areas of applied mathematics. Methods to calculate the matrix exponential and the sine and cosine matrix functions in terms of orthogonal matrix polynomials are introduced recently. In this chapter a method for computing hyperbolic matrix cosine and sine, based on Hermite matrix polynomial se...

Differential matrix models are an essential ingredient of many important scientific and engineering applications. In this work, we propose a procedure to approximate the solutions of special linear fourth-order matrix differential problems of the type Y (4)(x) = A(x)Y (x) + B(x) with higher-order matrix splines. An example is included.

RESUMEN Las escuelas del siglo XXI necesitan crear espacios que fomenten la creatividad, y a la vez debieran ser un modelo de innovación en el uso de las tecnologías con el fin de implementar con éxito las acciones que aseguren la calidad de la educación y la igualdad de oportunidades para todos los estudiantes; siempre resulta paradójico hablar de...

In this paper a method for computing hyperbolic matrix functions based on Hermite matrix polynomial expansions is outlined. Hermite series truncation together with Paterson-Stockmeyer method allow to compute the hyperbolic matrix cosine e ciently. A theoretical estimate for the optimal value of its parameters is obtained. An e cient and highly-accu...

This paper exposes the possibilities of creating a collaborative network website for our technologic and educational music project: Soundcool. It means a new model for music education based on the use of this application, a modular system with smartphones, tablets and Kinect developed by Universitat Politècnica de València (UPV) through several gra...

Soundcool is a collaborative system for sound and music creation using mobile phones, tablets, Kinect and MAX / MSP / Jitter. Soundcool is being developed at iTEAM under the direction of Dr. Jorge Sastre. Re-cently, two grants were awarded, one by Generalitat Valenciana to continue its development and the other grant by the Erasmus+ European progra...

This paper proposes a new model for music education based on the use of the application Soundcool, a modular system for music education with smartphones, tablets and Kinect developed by Universitat Politècnica de València (UPV) through UPV (2013, Spain) and Generalitat Valenciana (2015-2016, Spain) projects. Soundcool has been programmed in Max, a...

This work presents a new algorithm for matrix exponential computation that significantly simplifies a Taylor scaling and squaring algorithm presented previously by the authors, preserving accuracy. A Matlab version of the new simplified algorithm has been compared with the original algorithm, providing similar results in terms of accuracy, but redu...

The matrix exponential plays a fundamental role in linear differential equations arising in engineering, mechanics, and control theory. The most widely used, and the most generally efficient, technique for calculating the matrix exponential is a combination of "scaling and squaring" with a Pade approximation. For alternative scaling and squaring me...

“Music education is, in its nature, human and essentially serves to awaken and develop human capacities." This phrase by Edgar Willems (1890 - 1978) serves as a starting point in the design, implementation, tuning and validation of a digital interface for teaching and musical creation with children from 3 years old, visually impaired or affected by...

Hyperbolic matrix functions play a fundamental role in the exact solution of coupled partial differential systems of hyperbolic type. For the numerical solution of these problems, analytic-numerical approximations are most suitable obtained by using the hyperbolic matrix functions sinh(A) and cosh(A). It is well known that the computation of both f...

In this paper a method for computing hyperbolic matrix sine based on Hermite matrix polynomial expansions is presented. An error bound analysis is given.

This paper describes the objectives and work developed in the project New Technologies and Interfaces for Music Education and Production by Universitat Politècnica de València and the Computer Music Group from Carnegie Mellon University: Several education scenarios and application typologies are designed, the use of collaborative creation with Web...

Matrix functions have multiple applications in different areas of applied mathematics. Methods to calculate the matrix exponential and the sine and cosine matrix functions in terms of orthogonal matrix polynomials are introduced recently. In this chapter a method for computing hyperbolic matrix cosine and sine, based on Hermite matrix polynomial se...

This work gives a new formula for the forward relative error of matrix exponential Taylor approximation and proposes new bounds for it depending on the matrix size and the Taylor approximation order, providing a new efficient scaling and squaring Taylor algorithm for the matrix exponential. A Matlab version of the new algorithm is provided and comp...

Trigonometric matrix functions play a fundamental role in the solution of second order differential equations. Hermite series truncation together with Paterson–Stockmeyer method and the double angle formula technique allow efficient computation of the matrix cosine. A careful error bound analysis of the Hermite approximation is given and a theoreti...

Trigonometric matrix functions play a fundamental role in second order differential equation systems. This work presents an algorithm for computing the cosine matrix function based on Taylor series and the cosine double angle formula. It uses a forward absolute error analysis providing sharper bounds than existing methods. The proposed algorithm ha...

This work improves the scaling and squaring Taylor algorithm exptayns from a previous work with an improved theorem to bound the norm of matrix power series, a new formula for the Taylor approximation forward relative error, and the increase of the allowed bounds for the forward relative error in exact arithmetic with matrix size and approximation...

This paper presents an efficient method for computing approximations for general matrix functions based on mixed rational and polynomial approximations. A method to obtain this kind of approximation from rational approximations is given, reaching the highest efficiency when transforming nondiagonal rational approximations with a higher numerator de...

Differential matrix models are an essential ingredient of many important scientific and engineering applications. In this work, we propose a procedure to represent the solutions of first-order matrix differential equations Y′(x)=f(x,Y(x))Y′(x)=f(x,Y(x)) with approximate matrix splines. For illustration of the method, we choose one scalar example, a...

Using music to motivate the students’ learning in the first years of the School of Telecommunications Engineering (ETSIT) of the Technical University of Valencia (UPV) is the starting point of the presented experiences. From the study of concepts related to Circuit Theory, the implementation of a Post Graduate Degree in Electronic and Electroacoust...

The theremin is one of the earliest electronic musical instruments. It is named after the Russian physics Professor Lev S. Termen who invented it in 1919. This musical instrument belongs to a very short list of devices which are played without physical contact between the musician and the instrument. theremin players complain about the interference...

The matrix exponential plays a fundamental role in linear systems arising in engineering, mechanics and control theory. This work presents a new scaling-squaring algorithm for matrix exponential computation. It uses forward and backward error analysis with improved bounds for normal and nonnormal matrices. Applied to the Taylor method, it has prese...

Trigonometric matrix functions play a fundamental role in second order differential systems. In this article an efficient and highly-accurate Hermite algorithm is presented for the computation of matrix cosine. For an efficient evaluation of the polynomial approximation, the matrix is scaled and the Paterson-Stockmeyer’s method is applied. The doub...

This paper presents an application of Laguerre matrix polynomial series to the numerical inversion of Laplace transforms of matrix functions.

In this paper, we present a novel algorithm for precise eye detection. First, a couple of AdaBoost classifiers trained with Haar-like features are used to preselect possible eye locations. Then, a Support Vector Machine machine that uses Histograms of Oriented Gradients descriptors is used to obtain the best pair of eyes among all possible combinat...

In this paper, we introduce an improved bound on the 2-norm of Hermite matrix polynomials. As a consequence, this estimate enables us to present and prove a matrix version of the Riemann–Lebesgue lemma for Fourier transforms. Finally, our theoretical results are used to develop a novel procedure for the computation of matrix exponentials with a pri...

The matrix exponential plays a fundamental role in the solution of differential systems which appear in different science fields. This paper presents an efficient method for computing matrix exponentials based on Hermite matrix polynomial expansions. Hermite series truncation together with scaling and squaring and the application of floating point...

Many scientific and engineering processes are described by systems of linear first-order ordinary differential equations with constant coefficients, whose exact solution is given in terms of the matrix exponential, and a large number of methods for its computation have been proposed. This paper presents the key ideas for a competitive new scaling a...

This paper presents a new content-based method for real-time keyframe selection in H.264 low delay video coding. Based on dynamic thresholds, it is aimed at improving compression efficiency. It has been trained and tested with real sequences taken from movies and commercials, with very different motion and complexity characteristics, and from low t...

Information and Communications Technology (ICT) uses not to be vocational for students, moreover the presence that this technology has in society is general, but its knowledge is very superficial. The students of ICT sometimes need additional motivation since the concepts they study are complex and abstract. In this context the authors propose to i...

Las tecnologías de la Información y las Comunicaciones (ICT) no suelen ser vocacionales para los estudiantes, además la presencia de esas tecnologías en la sociedad está generalizada, pero su conicimiento es muy superficial. Los estudiantes, a veces necesitan motivación adicional ya que los conceptos que estudian son complejos y abstractos. En este...