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"The subject of multivariate splines has become a rapidly growing field of mathematical research. The author presents the subject from an elementary point of view that parallels the theory and development of univariate spline analysis. To compensate for the missing proofs and details, an extensive bibliography has been included. There is a presentation of open problems with an emphasis on the theory and applications to computer-aided design, data analysis, and surface fitting. Applied mathematicians and engineers working in the areas of curve fitting, finite element methods, computer-aided geometric design, signal processing, mathematical modelling, computer-aided design, computer-aided manufacturing, and circuits and systems will find this monograph essential to their research."

"kabupaten tertinggal merupakan kabupaten yang masyarakat serta wilayhnya relatif kurang berkembang dibandingkan daerah lain dalam skala nasional berdasarkan kategori perekonomian masyarakat, Sumber Daya Manusia (SDM), infrastruktur, kemampuan keuangan daerah, aksebilitas, dan karakteristik daerah. pengklasifikasian kabupaten tertinggal tidaklah mudah karena melibatkan variable dan observasi dalam jumlah yang cukup banyak. selain itu diantara variable yang digunakan memiliki keterkaitan antara satu dengan yang lain. MARS adalah salah satu metode pengklasifikasian yang mampu menangani data berdimensi tinggi dengan pola data yang tidak diketahui sebelumnya. dari model MARS yang dibangun, terdapat lima variable utama yang berpengaruh terhadap ketertinggalan kabupaten diantaranya adalah pengeluaran konsumsi per kapita, angka harapan hidup, persentase rumah tangga pengguna listrik, rata-rata jarak dari kantor desa/kelurahan ke kantor kabupaten yang membawahi, serta jumlah desa yang memiliki pasar tanpa bangunan permanen. akurasi dari model MARS yang terbentuk sangan tinggi, yakni mencapai 97,83 persen dan dapat dipergunakan untuk melakukan prediksi ketertinggalan kabupaten."

"Penelitian ini bertujuan untuk merumuskan model credit scoring untuk kredit mikro dengan menggunakan metode Multivariate Adaptive Regression Splines (MARS). Metode MARS merupakan pendekatan regresi nonparametrik yang memiliki kemampuan untuk memodelkan hubungan yang kompleks antar variabel tanpa asumsi model yang kuat dan menghasilkan model dengan akurasi tinggi yang melebihi model credit scoring lainnya dan mampu mengolah data berdimensi tinggi. Dalam beberapa tahun terakhir, MARS telah banyak diterapkan untuk memodelkan berbagai data, namun belum ditemukan penggunaanya untuk credit scoring kredit mikro. Secara umum metode credit scoring yang umum digunakan adalah analisis diskriminan dan regresi logistik. Namun kedua metode tersebut memiliki keterbatasan yaitu perlunya asumsi parametrik antara variabel respon dan prediktor. Penelitian menggunakan studi kasus data kredit mikro PT. Bank ABC yang merupakan market leader kredit UMKM di Indonesia. Hasil penelitian ini menunjukkan bahwa model penilaian kredit mikro dengan menggunakan MARS memiliki akurasi prediksi yang lebih tinggi dengan tingkat kesalahan terkecil, kesalahan tipe I dan II dibandingkan dengan Metode Regresi Logistik. Sehingga hasil penelitian ini dapat digunakan sebagai bahan pertimbangan bagi bank dalam menerapkan metode MARS dalam credit scoring dalam rangka pengendalian Risiko Non Performing Loan Kredit Mikro.

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This paper aim to formulate the credit scoring model for micro loan using the Multivariate Adaptive Regression Splines (MARS) method. The MARS method is a nonparametric regression approach that has the ability to model complex relationships between variables without strong model assumptions and produce a model with high accuracy that exceeds other credit scoring models and is able to process high-dimensional data. In recent years, MARS has been widely applied to model various data, but its use for micro loan credit scoring has not yet been found. Generally, the credit scoring methods commonly used are discriminant analysis and logistic regression. However, there are limitations to both methods, namely the need for parametric assumptions between the response variables and predictors. This study use a case study of micro loan data from PT. Bank ABC, which is the market leader for MSME loans in Indonesia.The results of this study indicate that the microcredit credit scoring model using MARS has a higher predictive accuracy with the smallest error rate, type I and II errors compared to the Logistics Regression Method. So the results of this study can be used as considerations for banks in applying the MARS method in credit scoring in order to control the Non-Performing Loan Risk of Micro Loan."

"This book presents methods of mathematical modeling from two points of view. Splines provide a general approach while compartment models serve as examples for context related to modeling. The preconditions and characteristics of the developed mathematical models as well as the conditions surrounding data collection and model fit are taken into account. The substantial statements of this book are mathematically proven. The results are ready for application with examples and related program codes given.In this book, splines are algebraically developed such that the reader or user can easily understand and vary the numerical construction of the different kinds of spline functions. The classical compartment models of the pharmacokinetics are systematically analyzed and connected with lifetime distributions. As such, parameter estimation and model fit can be treated statistically with a varied minimum chi-square method. This method is applicable for single kinetics and also allows the calculation of average kinetics.--"

"The finite element method (FEM) has become the most widely accepted general-purpose technique for numerical simulations in engineering and applied mathematics. Principal applications arise in continuum mechanics, fluid flow, thermodynamics, and field theory. In these areas, computational methods are essential and benefit strongly from the enormous advances in computer technology. B-splines play an important role in approximation and geometric modeling. They are used in data fitting, computer-aided design (CAD), automated manufacturing (CAM), and computer graphics. Finite Element Methods with B-Splines describes new weighted approximation techniques, combining the computational advantages of B-splines and standard finite elements. In particular, no grid generation is necessary, which eliminates a difficult and often time-consuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters. This is illustrated for typical boundary value problems in fluid flow, heat conduction, and elasticity.Topics discussed by the author include basic finite element theory, algorithms for B-splines, weighted bases, stability and error estimates, multigrid techniques, applications, and numerical examples. The text is essentially self-contained and easily accessible to graduate students in mathematics, engineering, and computer sciences. The new concepts are also of interest to academic researchers and to scientists in industry who are developing finite element software. Some basic facts on functional analysis and partial differential equations, which are required, are listed in the appendix."

"This book highlights new methods, algorithms and software for the digital processing and recovery of signals. In addition, it describes a new method for modeling one dimensional and multidimensional signals as successions of local polynomial splines and their spectral characteristics. It provides examples of how the proposed methods can be applied in specific cases, together with signal processing software examples in the MATLAB environment, and models of special processes in the Simulink environment. The books goal is to make it easier for beginners to understand the subject matter; it is intended for engineers, undergraduate and graduate students engaged in research or the evaluation and design of hardware and software for the digital processing and recovery of signals."